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 Topic: cosine
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 A triangular garden 2020-05-24 From yoonji:the 3 sides of a triangular garden measure 200 ft., 250 ft., and 300 ft., respectively. the garden is to be divided by a line bisecting the longest side and drawn from the opposite vertex. what is the length of the bisecting line?Answered by Penny Nom. An angle i a triangle 2020-05-16 From Ogunjobi:Two goal post are 8m apart a footballer is 34 m from one post and 38m from the other within what angle must he kick the ball if he is to scoreAnswered by Penny Nom. 0.366 x cos square (02 degree 17 mins 27 seconds) 2018-03-12 From michael:what is 0.366 x cos square (02 degree 17 mins 27 seconds) what is 0.366 x cos square (88 degree 26 mins 45 seconds)Answered by Penny Nom. A footballer angle 2018-02-14 From Kim:Two goal posts are 8m apart. A footballer is 34m from one post and 38m from the other. Within what angle must he kick the ball if he is to score a goal.Answered by Penny Nom. Solve the equation completely cos 2x = 1 2017-06-08 From Lava:Solve the equation completely cos 2x = 1Answered by Penny Nom. How far apart are the boats? 2016-12-13 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. ThanksAnswered by Penny Nom. Two airplanes 2015-04-14 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. Trig functions and the unit circle 2014-10-02 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. A triangular chicken pen 2014-04-27 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 2014-04-06 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. A triangle problem 2013-10-02 From raneem:ABC is a triangle in which : BC=20cm. M(infinity cos x 2006-12-07 From Katie:I was wondering if it was possible to find: lim x-->infinity cos x Answered by Stephen La Rocque. cos2x=1 2006-11-21 From Christina:I'm have a hard time solving cos2x=1 for exact values between 0<_x <360Answered by Stephen La Rocque and Penny Nom. A trig problem 2006-06-24 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 2006-06-14 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. The interior angles of a right triangle 2006-05-20 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. Solve the equation cos x = sin 20 where x is acute. 2006-03-26 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 2006-03-20 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. How do you find the angles in a triangle? 2006-01-27 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. The period of sin(x) + cos(x) 2005-07-21 From A student:WHAT IS THE PERIOD OF SIN(X)+COS(X)?Answered by Penny Nom. The tide at a boat dock 2005-01-11 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 2004-12-25 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 2004-10-30 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 = 20Answered by Harley Weston. Finding bearings 2004-05-24 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. Cosine of 35 degrees 2004-03-03 From Jason:How do you find the exact solution to cosine 35 degrees.Answered by Chris Fisher. Sin(3x), cos(3x) and tan(3x) 2004-01-28 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 cos4x- sin4x is the same as cos2x. Is cos8x-sin8x = cos2x also true? Thank you.sAnswered by Chris Fisher. Laws of sines and cosines 2003-11-23 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 2003-06-25 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 power-reducing 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 2003-06-10 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 2003-05-07 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) 2003-05-05 From A student:Write sin 2x in terms of sin xAnswered by Penny Nom. How far apart are the transmitters? 2002-05-18 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 2002-05-09 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. A trigonometric identity 2002-03-22 From Debby:I am stuck on a problem and wondering if you can help?? It is: Prove the following: sec2(X)+csc2(X) = sec2(X)csc2(X)Answered by Harley Weston. sin 2x = cos 3x 2002-02-25 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 2002-01-12 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 2002-01-12 From Justine:if you know that sin45degress = cos45degrees, how do you know that tan45degrees = 1?Answered by Penny Nom. A trig identity 2001-07-27 From Jeff:prove this identity and show steps tan(x/2+pi/4)=secx+tanxAnswered by Harley Weston. The speed of the boat 2001-07-12 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. The angles in a triangle 2001-05-11 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. The unit circle and trigonometry 2001-04-05 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 2001-02-21 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 2001-02-20 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. The laws of sines and cosines 2001-01-02 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 2000-11-29 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)/1-tan(x) cos(x)[ tan2(x)1-1]/cos2(x)+sin2(x)=sec(x) Answered by Harley Weston. Some trigonometry 2000-08-11 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). tan2(theta) = 3 I know sec2(theta) -1 = tan2(theta) ...Answered by Harley Weston. Using the inverse sine function 2000-05-31 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 180-x-y 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*((b2+c2-a2)/(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 3x-1=0 2000-05-11 From Cynthia:How would you solve 2sin 3x-1=0? I don't know what to do with the 3.Answered by Penny Nom. sin(7pi/12) 2000-05-04 From Kristel:What is the exact value of sin 7pi/12?Answered by Chris Fisher and Paul Betts. Triple angle formula 2000-02-23 From Sara:Can one derive a triple angle formula for sine and cosine? If so, how? Answered by Chris Fisher. A trig identity 2000-02-17 From Eric: Question: How do I solve this problem? ` sin3x cos3x _____ - _____ = 2 sinx cosx `Answered by Chris Fisher. Sines & cosine laws 1999-12-10 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 1999-12-01 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 1999-08-28 From Diane Simms:My question is can the following be factored. I am a teacher who needs the factors to this right away. 2 Sin2X + 2 SinX CosX - 1= 0 Answered by Harley Weston. From an airport control tower 1999-08-04 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 kindlyAnswered by Harley Weston. Sin 4A 1999-06-22 From Ryan Cochrane:If sinA = 4/5, and A is a first quadrant angle, find sin4AAnswered by Harley Weston. Cos(x) Cos(2x) Cos(4x)=1/8 1997-09-24 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 1997-06-23 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. 1997-06-09 From Vanessa Chan:Prove: arc cos4/5 + arc cos (-5/13) = arc cos (-56/65) Answered by Harley Weston. Ajax, Beverley, Canton and Dilltown 1997-03-14 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 1996-12-13 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 1996-11-07 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 1996-03-11 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 2006-02-19 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'est-ce qui fait que l'on trouve ce resultat??Answered by Claude Tardif.

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