







Solve the equation completely cos 2x = 1 
20170608 

From Lava: Solve the equation completely cos 2x = 1 Answered by Penny Nom. 





Selling price and markup 
20170424 

From Julie: What would the cost of an item be, if the sell price was $50 and the markup 48% Answered by Penny Nom. 





The cost of a piece of sheet metal 
20170414 

From Mohammed: I bought a 2 mm sheet plate of 1.2m × 2.4m in fijian $95. I used 1.95m × 0.4m from that sheet plate. What will be my total cost for the sheet plate I used. It was a mild steel plate. Answered by Penny Nom. 





How far apart are the boats? 
20161213 

From Halley: Two boats leave port at the same time. Boat A travels east at a speed of 12 km/hr. Boat B travels southwest at a speed of 14 km/hr. After two hours, how far apart are the boats? North is 0 degrees. How do I figure this out.
Thanks Answered by Penny Nom. 





Profit 
20160615 

From Toyia: 12.87 profit from 21.99 sale. What is the percentage that was taken off the 21.99 Answered by Penny Nom. 





The original price before a discount and taxes 
20151209 

From Michelle: Good day,
I would like to know if there is a particular equation to validate the following information:
I had to find the original cost of an item sold for 759.36$ before a 25% discount and 13% taxes.
I know we must use separate question to obtain the answer but I am unsure how to write the equation to validate my answer. Answered by Penny Nom. 





The amount before profit and overhead 
20150612 

From kelly: I have an existing amount of $22,750.00. this includes the profit at 10% and overhead at 10%.
How do I remove the profit and overhead in order to come up with the original starting figure? Answered by Penny Nom. 





A word problem 
20150508 

From JAMES: A businessman bought a number of similar articles for a total of sh. 6000. Three of the articles turned out to be defective with no resale value. He sold the remaining articles at 12.5% each above the cost price making a total profit of sh 480. How many articles had he bought? Answered by Penny Nom. 





Two airplanes 
20150414 

From john: two planes leave an airport at the same time, one going northwest (N35*W)at 400 mph and the other going east at 332 mph. How far apart are the planes after 4 hours to the nearest mile? Answered by Penny Nom. 





What is our cost? 
20150127 

From Johanna: I have a pieces of 3/4" sch40 (round tube) 240" long at $70. What is our cost. We also add 35% to our cost for selling price. How do I figure this out? Answered by Penny Nom. 





sin x = cos x 
20150123 

From Mubashir: there are two curves y=sinx and y=cosx intersecting at point where x is less than 90 and greater than 0.to find the point I made a equation sinx=cosx
but donot know what to do further .please help me by solving this equation sinx=cosx
also tell me that have you solved this equation by reference to the graph or by other means please do elaborate your solution in your answer. Answered by Penny Nom. 





Trig functions and the unit circle 
20141002 

From Jake: I was wondering what conclusions can be drawn about the trigonometric functions and how they work about the circle. Can you also please give me an explanation for it? Thank you. Answered by Penny Nom. 





Solve sin3x = cos2x 
20140714 

From Emanuel: If sin3x=cos2x, find the value of x when x<0<90' Answered by Penny Nom. 





A piecewise graph 
20140510 

From Zoe: Lightning Energy charges residential users for each unit of electrical energy bought from them each quarter, according to the scale below:
0500 units cost 17 cents per unit
5001500 units cost $85 plus 10 cents for each unit in the excess of 500
1500 or more units cost $185 plus 9 cents for each unit in excess of 1500
Sketch a graph showing the charge C as a function of U for up to 2000 electricity units Answered by Penny Nom. 





A triangular chicken pen 
20140427 

From Cierra: Margaret has two lengths of fence, 20 meters and 24 meters, for two sides of a triangular chicken pen. The third side will be on the north side of the barn. One fence length makes a 75° angle with the barn. How many different pens can she build if one fence is attached at the corner of the barn? What are all the possible lengths for the barn side of the pen?
Not sure what they are asking here... please show step by step what to do! Thank you so much! Answered by Penny Nom. 





The sides of a triangle 
20140406 

From Michael: I am supposed to sove for the length of side "b" of an irregular triangle. I am given the following:
Side a: 65'
Side b: Find this length
Side c: 50'
Angle A: unknown
Angle B: unknown
Angle C: 52 degrees
I am supposed to use the law of cosines to solve for side "b" and my teacher
says there is no mistake in the "givens" for the problem. I do not see how
this can be done using the law of cosines and i have not figured out how to sove for
angle B to use the law of cosines. Answered by Penny Nom. 





Converting cost per cubic yard to cost per ton 
20140205 

From Mayra: If 18 cubic yards= 25 tons and it's $28.00 per yard how much is it a ton. I need help please a refresher on my algebra. Thank you Answered by Penny Nom. 





A triangle problem 
20131002 

From raneem: ABC is a triangle in which : BC=20cm. M(<B) =29 and m(<C)=73 . D is the midpoint of BC
Find the length Of AB and AD approximated to 2 decimal places Answered by Penny Nom. 





If I know only the tax amount, how do I figure out total cost? 
20130811 

From Patric: If I know only the tax amount, how do I figure out total cost? Answered by Penny Nom. 





We can't write sinx and cosx as a finite polynomial. 
20130331 

From rimoshika: prove that we can't write sinx and cosx as a finite polynomial. Answered by Walter Whiteley. 





Your profit should be 20% of your cost 
20130221 

From anis: if the customer says your profit should be 20% of your cost..
1) my selling value should be cost +20% of cost = SP
or
2)cost / 0.80 = SP which is correct...if the second answer is right how should i justify my customer Answered by Penny Nom. 





The fourth side of an irregular polygon 
20130201 

From Emran: I have a irregular polygon. I know 3 of the 4 sides, and 2 of the angles. AB is 285, BC is 149, and CD is 310. Angle B is 135 degrees. and Angle C is 45 degrees. Is there a formula to solve for the final side? Thanks. Answered by Penny Nom. 





cos(theta/30) = 1 
20120514 

From Hope: cos (theta / 30 = 1
I am very confused as to how to solve it. Can you help? Answered by Penny Nom. 





Painting a pool 
20120325 

From Salai: A swimming pool measures 8m long, 6m wide and 1.5 m deep. The special paint for the pool cost $6per square metre.
How much will it cost to paint the interior surfaces of the pool ? Answered by Penny Nom. 





Tangent of theta 
20120117 

From stahl: explain what the 'tangent of theta' means. Draw and label a diagram to help with your explanation. Answered by Harley Weston. 





Three sides of a triangle 
20111224 

From saba: the three sides of a triangular lot have lengths 10,11and 13cm,respectively.
find the measure of its largest angle and the area of the lot? Answered by Penny Nom. 





What was the cost price of the article? 
20111110 

From tashana: By selling an article for $320,the profit was 20% of the cost price.what was the cost price of the article. Answered by Penny Nom. 





The cost of petrol 
20110826 

From Sam: Hi, i'm confused about this question from my textbook, here goes:
The cost of petrol for a 240 km journey for a car which runs 12 km on
each litre of petrol is $24. What would be the cost of petrol for a 500
km journey for a van which runs 11km on each litre of petrol?
please answer in detail and thanks in advance :) Answered by Penny Nom. 





Administration costs and profit 
20110405 

From brian: Hi , If I have direct job costs of $100. and my administration is 20 % and I want to make a 15 % profit , how would I calculate the administration and profit and what would be the total of each be and also the final total?
Thanks,
Brian Answered by Penny Nom. 





I need to make $1000 profit 
20110328 

From Kat: I need to make $1000 profit selling plants for $3 each. My direct cost is $2 per plant and my overhead is $5oo. How many pots (plants = 1 per pot) do I need to make $1000? Answered by Penny Nom. 





How much per ft. does it cost? 
20110314 

From Linda: 350 lbs. of coil at $1.80 per lb equals $630. each coil is 780 ft. how much per ft. does it cost? Answered by Penny Nom. 





The markup rate is 40% of the cost 
20110314 

From Abeth: A wallet sells for 450 pesos. the markup rate is 40% of the cost. find the cost of the wallet and markup. Answered by Penny Nom. 





How far must the pitcher travel to get to the ball? 
20101104 

From ken: A baseball player bunts a ball down the first base line. It rolls 35ft at an angle of 26 degrees with the first base path. The pitchers mound is 60.5 ft from the plate. How far must he travel to get to the ball. Answered by Penny Nom. 





Cost of a driveway 
20101011 

From arlene: What is the total cost of a driveway that is 25' wide and 45' long with 4" thickness if the concreat cost 92.00 per cubic yard and labor is 70.00 a cubic yard? Answered by Stephen La Rocque. 





Selling price, cost and profit 
20100622 

From Alex: The profit on a certain television set is 16.5% of the cost price. If the profit is $330,
Find:
a) the cost price
b)the selling price of the television Answered by Penny Nom. 





A radio tower 
20100326 

From Alex: The height of a radio tower is 450 feet, and the ground on one side of the tower slopes upward at an angle of 10 degrees. How long should a guy wire be if it is to connect to the top of the tower and be secured at a point on the sloped side 110 feet from the base of the tower? Answered by Harley Weston. 





A quadrilateral with 4 known sides and 1 known angle 
20100319 

From samuel: Name: Samuel
Status: Student
I have a quadrilateral with 4 known sides and 1 known angle, and I'm trying to evaluate the other angles of my quadrilateral.
By the law of cosines, I can easily find my opposite angle (using the diagonal as a basis for the equation).
However, to find the two remaining angles, I have found no other way so far than to use the other diagonal, which can be found with the equation attached (from geometry atlas).
Is there any simpler way? Answered by Robert Dawson and Harley Weston. 





Frank makes picture frames 
20100220 

From Carol: Frank makes picture frames his revenue from sales is R=$13.60x for frames sold. The cost making frames is C=$5.80x+$120 for frames made. What is the minum number of frames Frank must make and sell in order for his revenue to be greater than his costs. Answered by Penny Nom and Melanie Tyrer. 





Solving a triangle 
20100125 

From Paige: how do i solve a triangle with one angle of 73 degrees,
one angle of 32 degrees, and one side of 23cm? Answered by Harley Weston. 





The inradius of an icosahedron 
20100121 

From fnavroth: Suppose you have an equilateral triangle.
The area of the triangle is exactly 1200 square centimetres.
Now suppose you have twenty of those triangles.
It's possible to assemble those twenty triangles into a closed
threedimensional shape, a regular polyhedron.
What would be the volume, in cubic centimetres, of the largest sphere
that could fit inside the shape? Answered by Chris Fisher. 





A trig question 
20091215 

From A trig question: Hey, my name is Candle
I'm in academic math10 and am stuck on my trig... one question I thought I had right because i used the cosine law I got wrong and can't figure out why... here's a copy of the question. (i guessed it was D... but my teacher said it's B)
Thanks
Candle Answered by Robert Dawson. 





How fast is the distance between the two cars decreasing? 
20091208 

From Jenny: Two cares are on a collision course toward point P. The paths of the two cars make a 30 degree angle with each other. The first car is 40 km from P, and traveling toward P at 16 km/hour. The second car is 50 km from P, traveling at 20 km/hour. How fast is the (straight line) distance between the two cars decreasing. (Hint: Law of Cosines) Answered by Harley Weston. 





Integration of cos (x^2) dx 
20091012 

From Venkat: How do you evaluate the integration of cos (x^2) dx ? Answered by Harley Weston. 





Ordering pizza for 162 people 
20091001 

From Jean: Need to know how to feed about 162 people 70 square inches of pizza at the lowest price.
22" Pizza is $9.95
16" Pizza is $5.25
12" Pizza is $2.99 Answered by Penny Nom. 





Vectors and the Law of Cosine 
20090608 

From lauren: once force of 20 pounds and one force of 15 pounds act on a body at the same point so that the resultant force is 19 pounds. Find, to the nearest degree, the angle between the two original forces Answered by Janice Cotcher. 





Maximum profit 
20090511 

From Sally: a manufacturer of dresses charges $90 per dress up to 100 units and the average production cost is $60 per dress. to encourage larger orders the company will drop the price per dress by .10 for orders in excess of 100. I need to find the largest order the company should allow with the special discount to realize maximum profit. Answered by Harley Weston. 





Related rates 
20090309 

From Megan: A plane flying with a constant speed of 330 km/h passes over a ground radar station at an altitude of 3 km and climbs at an angle of 30°. At what rate is the distance from the plane to the radar station increasing a minute later? Answered by Harley Weston. 





Find the resultant of this displacement pair 
20090222 

From katydidit: Find the resultant of this displacement pair:
500 miles at 75 degrees east of north and
1500 miles at 20 degrees west of south.
How do I graph this and how do I solve this problem? Answered by Penny Nom. 





A Tshirt fundraiser 
20090111 

From Andre: Lou's class is selling Tshirts for a fundraiser. The supplier charges 750$ for the initial design and the setup plus 5$ for each imprinted shirt. The students sell the shirts for 15$ each.
a)How many Tshirts do the students need to sell to break even?
b)How much profit will the students make if they sell 150 shirts? Answered by Harley Weston. 





30% profit 
20090106 

From bob: this is a basic question that I just can't get thru my head.
I know all my cost for a product, if I want to sell at a given profit can I divide by a given
number, example for 30 % divide by .7 or do I multiply?
Is there a simple answer for this? Sure would make my work a lot easier.
Thank you for your time
Puzzled in Ohio Answered by Penny Nom. 





The angle between two lines 
20081217 

From abhi: how to calculate the angle between two lines, given the length of the lines..
angle should vary from 0  360 in the counterclockwise direction Answered by Robert Dawson and Harley Weston. 





The cost of a foundation 
20081208 

From carl: Hi, I need to work out the cost of a foundation.
The foundation is 1m deep x 500mm wide and is 6.3 meters long.
The cost per cubic meter for concrete is 1000 rand
escuvation of earth will be 100 rand per cubic meter and back filling wil also be
100 rand per cubic meter.
What will the cost be Answered by Harley Weston. 





The path of a small sailboat 
20081119 

From jane: a sailor in a small sailboat encounters shifting winds. she sails 2.00 km East
then 3.40 km North East, then an additional distance in an unknown direction. Her final position
is 6.68 km directly east of the starting point. find the magnitude & direction
of the third leg of the voyage. Answered by Harley Weston. 





How far are the boats apart? 
20081114 

From dom: Two boats leave port at the same time. They leave at 150 degree angle. One boat travels at 10mph and the other at 20mph. After two hours how far are the boats apart? Answered by Penny Nom. 





The angles and sides of a triangle 
20081113 

From JAMIE: a triangle with a side(b)37m an angle(C)70degrees and (a)79m find values of angles A and B and length of side c Answered by Stephen La Rocque. 





The cost of a steel plate 
20081105 

From Tammie: What is the formula to calculate the following:
I have a plate of steel that is 1/4" x 48" x 192" at a price of $15.23 per square foot
What is the formula to calculate the cost if I only use 1/4" x 471/4" x 681/8" of that steel plate? Answered by Penny Nom. 





How much does Luc pay for his tools?? 
20081020 

From imran: Luc makes $1 profit on each tool he sells. Marc makes a $2 profit while paying $5 less for his tools than Luc. Marc thus makes $6 more profit for every $100 invested. How much does Luc pay for his tools?? Answered by Penny Nom. 





The selling price 
20080904 

From Robert: Client wants to sell his property providing he is left with 100000.00$ net.
How do I calculate selling price if commission is 6% and taxes on the commission 6% Fed and 7.5%prov.
I'm taking the real estate class and this one really got me. Answered by Penny Nom. 





Radii and Chords Create a NonRight Triangle 
20080822 

From Beary: AOC is a diameter of circle O. Line AB is 12, and lines OA and OC (the radii) are 10. Find the length of line BO and chord BC. Answered by Janice Cotcher. 





Arclength and sectorangle 
20080806 

From Benson: If chord length, radius are given, How to find the sector angle and arclength Answered by Janice Cotcher. 





Guy wires for a tower 
20080519 

From larissa: a radio tower 500 feet high is located on the side of a hill ( the hill has an inclination to the horizontal of 5 degrees.) How long should two guy wires be if they are connected to the top of the tower and are secured at two points 100 feet directly above ( up the hill ) and directly below the base of the tower? Answered by Penny Nom. 





How many presses should be used? 
20080504 

From Sarah: Hi! I am in Calculus and this problem is on my study guide and i just cant figure it out!?
A printing company had eight presses, each of which can print 300 copies per hour. It costs $5.00 to set up each press for a run and 12.5+6n dollars to run n presses for an hour. How many presses should be used to print 6000 copies most profitably? Let h equal the number of hours used to print the 6000 copies. Answered by Harley Weston. 





Cost per square metre 
20080331 

From sandy: if something measures 7m x 3.6m with a depth of 1  1.5m and the total cost is 52 500.00, what is the cost per square metre Answered by Penny Nom. 





The profit was what percent of the cost? 
20080229 

From sierra: The profit was what percent of the cost?
Here is some more of that whole problem.
Selling Price$26.60
Discount$6.65
Sale Price after the Discount$19.95
The Profit$5.95 Answered by Penny Nom. 





The length of the third side of a triangle 
20080216 

From mary: I have an angle of 72 degrees and each of the sides are 5' long. What is the distance from each of the ends of the 5 feet to form a triangle. Answered by Stephen La Rocque. 





The cost before tax and shipping 
20080206 

From jonathan: Please explain how to solve this problem. I know you have to work backwards. If i have $125 to spend, how do I know the most I can spend before adding 6% tax and 9% shipping.(shipping is cost before tax) I can only figure this out by trial and error. I know there is a better way Answered by Penny Nom. 





Tiles on a basement floor 
20080131 

From ORIETTA: I have a basement 1000 sq ft I want to purchase tile that are 18x18inches
and they are charging 4.15 sq ft how much would it cost since I will need
less tiles to cover the area since it's not 12X12 Answered by Penny Nom. 





The cosine of an angle 
20080121 

From Kristine: Find measure of unknown side
cosA=0.5 Answered by Harley Weston. 





The angles of a triangle given the three sides 
20080117 

From Lucy: Is there a way to find the angles of a triangle just by knowing the lengths of it's sides?
It seems like the would be a relationship between the two, but I'm not sure. Answered by Stephen La Rocque and Harley Weston. 





How far is the jet from the lighthouse? 
20080107 

From Natalie: Question: A ship spots a lighthouse that is 53m high, at an angle of elevation of 7 degrees that is directly north of the ship. The same ship spots a jet travelling N62E at an altitude of 1500m with an angle of elevation of 15 degrees. How far is the jet from the lighthouse?
Natalie Answered by Harley Weston. 





sin^2x=1/2(1cos2x) 
20071212 

From katelyne: Hello there.. I was assigned a problem that I am having trouble with in my
PreCalc class and it is as follows:
sin^2x=1/2(1cos2x) Answered by Penny Nom. 





How many houses must they paint? 
20071212 

From Natalie: The question is: Four boys work together,painting houses for the summer.For each house they paint they get 256 pounds.
If they work for four months of the summer and their expenses are 152
pounds per a month, how many houses must they paint for each of them
to have one thousand pounds at the end of the summer? Answered by Penny Nom. 





What would be the cost of a 10 in * 15 in canvas? 
20071201 

From Jasmine: a 40in *60 in canvas is sold for $60.00 if the price is determined by the cost of the material what would be the cost of a 10 in * 15 in canvas Answered by Stephen La Rocque. 





The definition of the sine function 
20071122 

From Indrajit: I need a explanation in this theory.......if sinθ = p/h...then
sin 90 deg. = p/h
or 1 = p/h
or p=h .....how can a perpendicular be equal to a hypotenuse.??? Answered by Harley Weston. 





Area of a quadrilateral 
20071010 

From Courtney: how would i find the area of a quadrilateral..
the sides are a (/) is 6cm, b (—) is 9 cm, and c (\) is 7 cm..
the angle between a and b is 140 degrees and b and c is 115 degrees.. Answered by Stephen La Rocque. 





Maximizing profits II 
20071005 

From a student: Suppose there are three firms with the same demand function. The function is Q=100040P. Each firm also a a cost function.
Firm 1: 4000+5Q,
Firm 2: 3000+5Q,
Firm 3: 3000+7Q.
What price should each firm charge if it wants to maximize profits. Answered by Harley Weston. 





Breaking even 
20070816 

From virginia: a company that manufactures bikes has a fixed cost of $100,000.00 it costs $100 to produce each bike. the selling price per bike is $300.00
write the cost function, c
write the revenue function, r
determine the break even point Answered by Leeanne Boehm and Steve La Rocque. 





The length of the third side of a triangle 
20070815 

From Brooklyn: What is the equation to find the length of the third side of a triangle if you have the length of A, B, and the angles(s)? Answered by Stephen La Rocque. 





The cost of some groceries 
20070718 

From A student: Two boxesof the cereal and our four cans of the pears were boutht at grocery store,the cereal cost $2.29per box and the pears cost 79cent per can.sales tax is 6% what was the total cost of the food diregerding ? Answered by Penny Nom. 





Calculating the area (acreage) of a four sided lot 
20070718 

From A property owner: I have a real estate property and the lot size is something I need to find out. I know the lengths of the four sides, but it isn't a rectangle, it is an odd shape. How do I find the acreage? Answered by Stephen La Rocque. 





Trig functions for angles not between 0 and 90 degrees 
20070716 

From Tim: My question: Why is the value of a trigonometric function, the same, for an angle over 90 degrees and its reference angle?
How are the angle and its reference related? Do they both form a triangle that has equal sides? Answered by Penny Nom. 





Any regular polygon inscribed in a circle 
20070712 

From DJ: Circle with r=12" is inscribed in a regular octagon. What is the length of each octagon segment?
Note: Our answer works for any regular polygon inscribed in any circle. Answered by Stephen La Rocque. 





sinx and cosx 
20070625 

From Mac: Can anyone tell me whether sinx and cosx is differentiable at x=0 ?
As far as i know, cos(x) and sin(x) is differentiable at all x. Answered by Penny Nom and Stephen La Rocque. 





The area of a quadrilateral 
20070610 

From Lucy: Calculate the area of the quadrilateral ABCD.
AB= 4.1cm, BC = 7.6cm, AD= 5.4 cm, CD= ?
Angle ABC = 117, Angle ADC = 62.
Give your answer correct to 3 significant figures. Answered by Stephen La Rocque and Penny Nom. 





The cost of laying cable 
20070605 

From Gilligan: MetroMedia cable is asked to provide service to a customer whose house is located 2 miles from the road along which the cable is buried.
The nearest connection box for the cable is located 5 miles down the road. If the installation cost is 10 dollars per mile along the road and 14 dollars per miles off the road, express the total cost C of installation as a function of the distance x (in miles) from the connection box to the point where the cable installation turns off the road. Give the domain.
Also, compute the cost if x = 1 mile and if x = 3 miles.
In order to use the given values for x, do I need a formula?
If so, what is that formula?
I can take it from there. Answered by Stephen La Rocque. 





If I know the total is 15% over cost, what is the cost? 
20070518 

From Theresa: I have a job that is $25,250 total to complete the job. The customer asked how
much am I charging. I told him I was charging 15% over the Cost. What is the
formula to calculate the cost of the job? Answered by Stephen La Rocque. 





Evaluating sine and cosine 
20070506 

From Selimovic: How can i solve sine or cosine for angle of, lets say 10°....Maybe
it's easy but i don't know how... Answered by Penny Nom. 





The law of cosines 
20070323 

From chetna: Q 1) In triangle LMN, l=7, m=5 , n=4. find ANGLE N.
After applying the rule and substituting values i'm getting
Cos n= 58/40. Is there something wrong. The answer at the back of the book is 34 degrees. Answered by Penny Nom. 





Cost of ribbon 
20070320 

From kelly: we are doing rate
Ribbon costs $1.44 for 3m
a). What is the cost per meter?
b). How much would 5 m of ribbon cost?
c). How much ribbon could you buy for $12.00 Answered by Penny Nom. 





Cost per square foot 
20070214 

From llinden: how do you figure out the cost of square footage? the amount per sq ft is $28 Thank you Answered by Gabriel Potter. 





A curve on a cylinder 
20070127 

From John: think of a tube,say 50mm in diameter made out of cardboard, project vertical lines at right angles from the base at say every 2mm right round the tube in pencil.No pretend you can put this cardboard tube in a saw and cut it at 45degrees. Get a pair of scissors and cut it at the lowest end and lay it out flat.It now looks like a graph,how do you work out each of these vertical lengths possibly chord lengths Answered by Stephen La Rocque and Penny Nom. 





lim x>infinity cos x 
20061207 

From Katie: I was wondering if it was possible to find: lim x>infinity cos x Answered by Stephen La Rocque. 





cos2x=1 
20061121 

From Christina: I'm have a hard time solving cos2x=1 for exact values between 0<_x <360 Answered by Stephen La Rocque and Penny Nom. 





What is the total cost of a driveway ... 
20060829 

From Ismael: What is the total cost of a driveway 15' wide, 40' long and 4" thick if the concrete costs $60.00 per cubic yard and the labor costs $1.25 per square foot? Answered by Stephen La Rocque. 





Minimizing a cost 
20060725 

From Edward: The cost of running a car at an average speed of V km/h is given by c= 100 + (V2 / 75) cents per hour. Find the average speed (to the nearest km/h) at which the cost of a 1000 km trip is a minimum. Answered by Stephen La Rocque. 





54x14x8 at $28.00 per cubic foot 
20060724 

From Toi: How much would it cost if I had an item that was 54x14x8 and it was $28.00 per cubic foot? Answered by Stephen La Rocque. 





A trig problem 
20060624 

From Greg: A and B are two towers, B being 4 km due east of A. The true bearings of a flagpole, C, from A and B are α east of north and α west of north respectively. The true bearings of a second flagpole, D, from A and B are (α + β) east of north and (α  β) west of north respectively. Assuming A, B, C, and D are on level ground, and that α = 25, β = 10, find the distance between C and D. Answered by Penny Nom. 





The chord length of a polygon 
20060614 

From Krishna: I have to find out the chord length of a polygon  Tetradecagon ! The Radius of the Circle is 11.5 Cms. The Circle is intersepted by 14 arcs. Then how to find out the chord length? Answered by Stephen La Rocque. 





Tiling a floor 
20060608 

From Marguerite: A builder is adding a 20' X 28' addition to a house. He has two choices: he can use 8" X 8" tile @ $.98 a tile or 12" X 12" tile @ $1.98 a tile. How much money would he save by using the least expensive choice? Answered by Stephen La Rocque and Penny Nom. 





Can you explain the differences between margin and mark up? 
20060607 

From Michelle:
I have a widget I buy for $10. I want to make a 40% margin on the product cost. What do I then sell to the customer for?
Also, can you explain the differences between margin and mark up?
Answered by Penny Nom. 





What is the value of csc (2pi/3)? 
20060604 

From Kishor: What is the value of csc (2pi/3)? Answered by Stephen La Rocque. 





The interior angles of a right triangle 
20060520 

From Greg: I am wondering if there is a way to figure out the interior angles of a right triangle if we know ONLY the side lengths, and the trick is, we CANNOT use arctangent! Answered by Leeanne Boehm and Penny Nom. 





The radius of a soccor ball 
20060505 

From Jacqui: A soccer ball is made up of hexagons and pentagons with the same side lengths.
A manufacturer wants to produce a ball of certain diameter. The questions that follows is what side length for the polygons will produce a ball of certain diameter. Answered by Chris Fisher. 





What is the original cost? 
20060419 

From Charlie: Selling a piece of furniture for $670 and the profit is 35%. What is the original cost? Answered by Stephen La Rocque. 





What is the cost price? 
20060414 

From Purushotham: If the selling price is 120 and the profit is 20%, what is the cost price? Answered by Stephen La Rocque. 





cos(3X) 
20060329 

From Joshua: I'm having trouble proving that cos(3X)=cos^{3}X (cosX)(sin^{2} X) Answered by Penny Nom. 





The cost of pizza 
20060328 

From Kristine: Use the formula for the area of a circle, A=3.14rsq, to determine which is a better deal: a 14in. pizza for $10.50 or a 16in. pizza for $11.95. Using 3.14 for pi Answered by Penny Nom. 





Solve the equation cos x = sin 20 where x is acute. 
20060326 

From Elle: Solve the equation cos x = sin 20 where x is acute. Answered by Stephen La Rocque. 





Three towns are located at the vertices of an equilateral triangle 
20060320 

From A student: three towns are located at the vertices of an equilateral triangle. The towns are 8, 5, and 3 miles, respectively, from a store. How far apart are the towns? Answered by Chris Fisher. 





Adding a cellar 
20060314 

From Spencer:
You want to add a cellar to your store. The construction company told you it would cost $5.90 per cubic yard to dig the cellar plus $20.00 per square ft. to finish it.
How much will it cost to add a cellar 36 feet long, 14 feet wide, and 8 feet deep?
Answered by Stephen La Rocque. 





Profit 
20060225 

From Vernessa: ABC company wants to sell enough products to earn a profit of $40,000, if unit sales are $10 and variable costs $8 , fixed cost $80,000 how many units must be sold to earn a profit of $40,000. Answered by Penny Nom. 





How do you find the angles in a triangle? 
20060127 

From Keith: How do you find the angles in a triangle if you know the lengths of the sides? Answered by Chris Fisher and Penny Nom. 





Brochure cost 
20051102 

From Duk: The organizers of the walkathon want to have brochures printed to advertise the event. They get cost estimates from two printing companies. The costs are given by the equations.
Company A : C= 15 + 0.10n
Company B : C= 0.25n
For what number of brochures is the cost the same for both companies? Answered by Penny Nom. 





Marked down 31% 
20051027 

From Virginia:
Question: How do you calculate a percentage back into a cost?
Example: $1,025.00 sale cost and I want to add 31 percent back into it for a list cost.
Answered by Penny Nom. 





Painter's caps 
20051019 

From Duk: The equation C=10 +2n represents the cost in dollars, C, for n painter's caps advertising the walkathon. Which pair of values could represent a number of caps and the cost for that number of caps, (n, C)?
(0, 10) (7, 24) (15, 30) Answered by Penny Nom. 





The period of sin(x) + cos(x) 
20050721 

From A student: WHAT IS THE PERIOD OF SIN(X)+COS(X)? Answered by Penny Nom. 





arccos(5/13) 
20050531 

From Kyle: I would like to know how to evaluate the problem of: Arccos 5/13. Answered by Penny Nom. 





Cost price 
20050525 

From Sunitha: What is (how to calculate) the cost price of a product which is markedup by 15% and retailed at $25? Answered by Penny Nom. 





The cost of concrete 
20050308 

From Cathy: Compute the cost of ready mixed concrete for a driveway 70ft long, 10ft wide, 3 inches deep at a cost of $30.00 per cubic yard Answered by Penny. 





The tide at a boat dock 
20050111 

From Abraham: The tide at a boat dock can be modeled by the equation
y = 2cos(pi/6 t) + 8,
where t is the number of hours past noon and y is the height of the tide, in feet. For how many hours between t=0 and t=12 is the tide at least 7 feet? Answered by Penny Nom. 





Modelling monthly temperature with a cosine 
20041225 

From Regis: The average monthly temperature for a location in Ontario as a function of month number can be modelled using the equation y = a cos[k(t + b)] + d. Answered by Harley Weston. 





Solving triangles 
20041030 

From Allen: Solve the following triangles.
Given
1. B = 20 Degrees, a = 25, b = 16
2. A = 35 Degrees, b = 2, c = 3
3. A = 32 Degrees, C = 44, c = 20 Answered by Harley Weston. 





Finding bearings 
20040524 

From James: This question is about finding bearings. A boat race starts from point A, goes North to Point B, a distance of 1000 meters. The course is triangular. The bearing from point B to point C is South 70degrees West. The distance from Point B to point C is 1500 meters. Find the course bearing from C to A.
Answered by Penny Nom. 





Some ratio problems 
20040313 

From Hossen:
1) After James spent 2/5 of his pocket money on magazines, and 1/4 of his pocket money at a football match, he had £1.75 left. How much pcket money did he have in the beginning?
2) A joint of Lamb costs £5.95 per/kg. The price per kilogram is reduced. A joint weighing 1.2kg is reduced by 50p.
A) What is the reduced price per kilogram?
c Answered by Penny Nom. 





Cosine of 35 degrees 
20040303 

From Jason: How do you find the exact solution to cosine 35 degrees. Answered by Chris Fisher. 





Sin(3x), cos(3x) and tan(3x) 
20040128 

From Jon: What is the identity for cos3x, sin3x, and tan3x? In class, we learned double angel identities and were asked to find out the identity to these three trig functions. If you can help, please do. Also, i know that the cos^{4}x sin^{4}x is the same as cos2x. Is cos^{8}xsin^{8}x = cos2x also true? Thank you.s Answered by Chris Fisher. 





Room and board fees 
20031129 

From Jennifer: A certain university wishes to determine room and board fees for the next academic year. For the current year, the fee is $3600 per student and 1800 students are living in the residence halls. Past data suggests that for every $300 increase in the semester fee, 200 fewer students will choose to live in the dorms. There are also costs to the university associated with the residence halls. The fixed costs total $2,000,000 per semester. the variable costs are currently $1000 per student but will fall $100 per student for each decrease of 100 students. Your task is to help the university determine the optimal fee. Assume linear relationships between the number of students and the fee and between the number of students and the cost per student Answered by Penny Nom. 





Laws of sines and cosines 
20031123 

From A parent: On the one side of a stream lines PA= 586.3 feet, PB = 751.6 feet are measures, angle APB being 167 degrees and 36 min. Q is a point on the opposite side of the stream. Angle PAQ=63 degress and 18 min and PBQ=49 degrees and 24 min. Find PQ. Answered by Penny Nom. 





Odd powers of sine and cosine 
20030625 

From Antonio: Can you please tell me how to integrate a trig function involving sine and cosine? I know if the powers of both the sine and cosine are even and nonnegative, then I can make repeated use of the powerreducing formulas. But for the question I have on my hand, the powers of both sine and cosine are odd: ( sin3x + cos7x ) dx. Answered by Harley Weston. 





Two trig problems 
20030610 

From Bett:
I have this ongoing trouble with trig and solving triangles with laws of cosines and sines!! For example if it asks to solve triangle FGH, given angle G=102.7 , side f=14.2, and h=18.6. Now do I use law of cosines because I don't have the measure of an angle and length of the opposite side??I don't know where to go from here,I am totally confused!!! I also have a problem with this word problem I have been doing. It asks: An airplane flies 847.5 km at a bearing of 237.3 degrees. How far south and west fo its original position is it? Huh? Please help! Answered by Penny Nom. 





sin theta = 7/8 
20030507 

From Patty: If sin0 = 7/8 and 0 is in quadrant 2, find the other five trigonometric functions of 0. (report your answers in radical form) Answered by Penny Nom. 





Write sin(3x) in terms of sin(x) 
20030505 

From A student: Write sin 2x in terms of sin x Answered by Penny Nom. 





Which is the better buy? 
20021204 

From Lynda: my question is the big can held 18 ouces and cost $2.52.The small can held only 12 ounces and cost $1.08. Find both unit prices. which can was better buy? Answered by Penny Nom. 





How far apart are the transmitters? 
20020518 

From Jeff: A ship at sea is 70 miles from one transmitter and 130 miles from another. The measurement of the angle between the signals is 130 degrees. How far apart are the transmitters? Answered by Penny Nom. 





The law of cosines and obtuse angles 
20020509 

From Bryant: The question that I am pondering is that I need to derive the law of cosines for a case in which angle C is an obtuse angle. Answered by Penny Nom. 





Sodding the yard 
20020408 

From Craig: my parents want to lay sod in our back yard. the sod cost $2.00 per square foot. The size of our yard is 20x20 and 26x41 Answered by Penny Nom. 





A trigonometric identity 
20020322 

From Debby: I am stuck on a problem and wondering if you can help?? It is: Prove the following: sec^{2}(X)+csc^{2}(X) = sec^{2}(X)csc^{2}(X) Answered by Harley Weston. 





sin 2x = cos 3x 
20020225 

From Allan: solve: sin 2x = cos 3x Primary question: how do you handle the cos 3x? Answered by Paul Betts and Chris Fisher. 





Adding vectors 
20020112 

From Lena: how do you add vectors together? If you are given the length and angles of both vectors and are asked to add/subtract them, how do you do it? I know you are supposed to do the head to tail method, but whenever i try it i get the wrong answer. I need help setting it up. example: A is 2.7cm, and 60 degrees, B is 1.6cm and 135 degrees, find the magnitude and amplitude Answered by Penny Nom. 





The tangent function 
20020112 

From Justine: if you know that sin45degress = cos45degrees, how do you know that tan45degrees = 1? Answered by Penny Nom. 





Catenary 
20020102 

From Jason: I am a high school math teacher. I was asked by a friend who is in architectural design for a method for determining the volume of what he called a Catenary. The Catenary curve is modeled by the equation y=a cosh(x/a). I ran into a mess when I tried to compute the volume of the solid formed by revolving that curve around the yaxis. Any help you can provide would be greatly appreciated. Answered by Harley Weston. 





A trig identity 
20010727 

From Jeff: prove this identity and show steps tan(x/2+pi/4)=secx+tanx Answered by Harley Weston. 





The speed of the boat 
20010712 

From Sharon: A motor boat is travelling in a southeasterly direction in water that is flowing from the south at 2km per hour. Show that the speed of the boat is (6 times the square root of 2) km per hour, given that it can travel at 10km per hour in still water. Answered by Penny Nom. 





A phone bill 
20010618 

From Janet: What is the formuala to calculate cost per minute? Here is the data below # of calls  238 # of minutes  443 cost  $70.06 Answered by Penny Nom. 





The angles in a triangle 
20010511 

From Nikki: Find the measure, to the nearest degree, of each angle of a triangle with sides of the given lengths. 26, 35, 40 Answered by Penny Nom. 





Maximize profit 
20010509 

From Brian: The marginal cost for a certain product is given by MC = 6x+60 and the fixed costs are $100. The marginal revenue is given by MR = 1802x. Find the level of production that will maximize profit and find the profit or loss at that level. Answered by Harley Weston. 





The unit circle and trigonometry 
20010405 

From Ashley: "My teacher wants us to find out what a unit circle is, which I found out, a circle with the radius of 1, but the problem is he wants us to show the relationship between the unit circle and the sine(30,45,60 degrees), cosine(30,45,60 degrees),and tangent ratios(30,45,60 degrees). I need help with this and my teacher will not help us out. Thanks very much ... Answered by Penny Nom. 





The law of cosines in the real world 
20010221 

From Hope: Do you have any examles and/or labs that show how the law of cosines is used in the real world? Answered by Harley Weston. 





Law of cosines 
20010220 

From Emily: I missed a few days of class and I can't figure out how to solve Law of Cosines problems. I have the notes and formulas but I can't figure out how to do the math involved to answer the problems. I am also getting confused about how to use degrees and seconds in the Law of Sine and Cosine. I can't seem to get the correct answers and I don't really know how to solve them and enter them into my TI 86. Answered by Harley Weston. 





Delivering firwood 
20010220 

From Jackie: Two college students earn extra money on weekends by delivering firwood in thier pickup truck. They have found that they can sell x cords per weekend at a price of p dollars per cord, where x=753/5 p. The students buy the firewood from a supplier who charges them C dollars for x cords to the equation C=500+15 x+1/5 x^{2}.
a) find a function f such that P=f(p), where P dollars is the profit per weekend for the students if they charge p dollars per cord.
b)find the profit P dollars if p=$95 Answered by Penny Nom. 





The laws of sines and cosines 
20010102 

From Faydene: Can the sine /cosine rule be applied to a right angle triangle to find a particular solution or are these 'rules' applied only when the triangle is not right angled? Answered by Penny Nom. 





Trig identity crisis 
20001129 

From Rhiannon: I have tried many times to find the answer to these problems but I can't I am in grade 12  tan(x)=csc2(x)cot2(x)
 cos(x)/csc(x)2sin(x)=tan(x)/1tan(x)
 cos(x)[ tan^{2}(x)11]/cos^{2}(x)+sin^{2}(x)=sec(x)
Answered by Harley Weston. 





Some trigonometry 
20000811 

From Angela: I have some PreCal questions. I am a student at the secondary level. I would be very grateful for your help. Solve the equation for theta (0 <= theta < 2pi). tan^{2}(theta) = 3 I know sec^{2}(theta) 1 = tan^{2}(theta) . . . Answered by Harley Weston. 





Using the inverse sine function 
20000531 

From Nelson Rothermel: This has me completely baffled. I have to use the laws of sine or cosine to find the angles of a triangle when I have 3 sides, so I can't go 180xy when I have 2 angles. Now, I have a triangle with values of 3, 7, and 9. Here are the steps I used (A,B,C are angles; a,b,c are opposite sides): angle A (16.1951 degrees): cos^{1}*((b^{2}+c^{2}a^{2})/(2*b*c)) angle B (40.6011 degrees): sin^{1}*(b*sin(A)/a) angle C (56.7962 degrees): sin^{1}*(c*sin(A)/a) If you notice, A+B+C does not equal 180. According to the book, A and B are correct, but C is supposed to be 123.2038 degrees. Why doesn't it work??? Answered by Harley Weston. 





Solve 2sin 3x1=0 
20000511 

From Cynthia: How would you solve 2sin 3x1=0? I don't know what to do with the 3. Answered by Penny Nom. 





sin(7pi/12) 
20000504 

From Kristel: What is the exact value of sin 7pi/12? Answered by Chris Fisher and Paul Betts. 





Triple angle formula 
20000223 

From Sara: Can one derive a triple angle formula for sine and cosine? If so, how? Answered by Chris Fisher. 





A trig identity 
20000217 

From Eric:
Question: How do I solve this problem? sin3x cos3x _____  _____ = 2 sinx cosx Answered by Chris Fisher. 





Sines & cosine laws 
19991210 

From Pierre Boivin: Triangle LMN, angle L=71 degree , LM= 7.2 , MN=8.3 , ln= 5.9 The questiion was to find angle M. Using the cosine law I found the answer to be 44 degree. It is also the book answer. Using the sines law I found the answer to be 42.2 degree. why can't I use the sines law. Answered by Chris Fisher. 





Cos x = 1/2 
19991201 

From Pierre Boivin: When I factor[ 2cos (square)  5cos 3], I get (2cos + 1)(cos  3). 2cos + 1 = 0, 2cos = 1, cos = 0.5,. Using inv cos on calculator, I get 120 degree related angle. When I graph I get two values, between 90 and 180 degree and between 180 and 270 degrees. How do I find those two values. How do use 120 degree in relation with the x axis. Answered by Penny Nom. 





A Trigonometry Question 
19990828 

From Diane Simms: My question is can the following be factored. I am a teacher who needs the factors to this right away. 2 Sin^{2}X + 2 SinX CosX  1= 0 Answered by Harley Weston. 





From an airport control tower 
19990804 

From Pammy: Hi I am a 30 yo mature age student doing my HSC but am having difficulty understanding this, if you can help me. From an airport control tower, a Cessna bears 023 degrees T and is 27km away. At the same time, a Boeing 767 bears 051 degrees T and is 61km from the tower. Both planes are at the same height. i) What is the size of angle ATB? ii) Using the cosine rule to calculate the distance the planes are apart, to nearest kilometre. I figured out and drew the triangular diagram but can't figure out the rest and which formula to use. sorry about this, thankyou kindly Answered by Harley Weston. 





Staying under budget. 
19990622 

From Chris: If I had $147.69 and I had to buy 200 bannas at $.46 & 100 potatos at $.42 each how do I stay under my buget Answered by Penny Nom. 





Sin 4A 
19990622 

From Ryan Cochrane: If sinA = 4/5, and A is a first quadrant angle, find sin4A Answered by Harley Weston. 





A rhombicosidecahedron 
19990430 

From Himmat: What is a rhombicosidecahedron? Answered by Harley Weston. 





Platonic Solids Surface Area 
19981202 

From Rachel Bidwell: How do you find the surface area of the 5 platonic solids, when they each have a volume of one cubic inch Answered by Harley Weston. 





Cos(x) Cos(2x) Cos(4x)=1/8 
19970924 

From Tan Wang: How many distinct acute angles x are there for which cosx cos2x cos4x=1/8? Answered by Chris Fisher Harley Weston and Haragauri Gupta. 





Finding the Mine 
19970623 

From Billy Law: Tom is gold prospector. On his last trip out from town, he headed 35 degree South of West to a lake where he had lunch. The lake was 24 km out of Town. He then headed due East for 35 km before Doubling back on bearing of 15 degree South of west for 20 km to reach his mine. By converting to Cartesian coordinate before doing vector additions do the following: a) Calculate the position of the mine from town in term of a distance and a direction. ... Answered by Harley Weston. 





A problem with arccos. 
19970609 

From Vanessa Chan: Prove: arc cos4/5 + arc cos (5/13) = arc cos (56/65) Answered by Harley Weston. 





Ajax, Beverley, Canton and Dilltown 
19970314 

From S. Johnson: The following towns are placed on a coordinate system. Ajax at (x,z), Dilltown at (10,0), Canton at (0,0) and Beverly at (0,10). The roads from Beverly to Canton and from Canton to Dilltown are perpendiculat to each other and are each 10 miles in length. A car traveling at all times at a constant rate, would take 30 minutes to travel straight from Ajax to Canton, 35 minutes to travel from Ajax to Canton via Beverly, and 40 minutes to travel from Ajax to Canton via Dilltown. What is the constant rate of the car, to the nearest tenth of a mile per hour. Answered by Chris Fisher and Harley Weston. 





A trig problem 
19961213 

From S. Johnson: sin t + cos t = 1/5. Find ALL exact values of cot t, given the original equation. Answered by Harley Weston. 





Height of a Hotel 
19961107 

From Irene: "Irene" is to determine the # of floors in a hotel 500 feet up the street. Irene is on the 10th floor of an office building and can measure the angle of elevation to the top of the hotel, 57 degrees. Her view of the entire building is obstructed. If the street rises at an angle of 8 degrees from the office building to the hotel and the average distance between floors is 11 feet, how many floors are on the hotel? Answered by Penny Nom. 





A trig identity 
19960311 

From Azmat Hussain: Is there an easier/another way to prove the trig identity cos(a+b) = cos(a)cos(b)sin(a)sin(b)? Answered by Penny Nom. 





probleme sin cos 
20060219 

From Thibault: mon probleme commence par: f(x)=sinx (sinx+1)+ cos²x
donc en le dévellopant on trouve: f(x)= sin²x + sinx + cos²x
et apres ce que je ne comprend pas est que par la suite on trouve: f(x)= 1+sinx
qu'estce qui fait que l'on trouve ce resultat?? Answered by Claude Tardif. 





Un polyedre ayant comme face 20 triangles 
20000802 

From Sonia: J'aimerai savoir comment s'appelle un polyedre ayant comme face 20 triangles équilatéraux égaux. Answered by Chris Fisher. 

