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A tangent to a curve 2017-10-22
From Jasem:

Suppose that
f(x)=(3x-3)^1/2.

(A) Find an equation for the tangent line to the graph of f(x) at x=2

(B) Find all values of xx where the tangent line is horizontal, and enter them as a comma-separated list (e.g., 2,-3,6). If there are none, enter none.

Values of x


Answered by Penny Nom.
Two tangent circles 2016-11-27
From mikee:
find the equation of a circle tangent to the circle x2+y2=4 and with the center at (0,5)
Answered by Penny Nom.
tan15 2016-04-11
From JOHN:
find the exact value of tan15 in surd form.
Answered by Penny Nom.
tan inverse 1/4 2016-03-14
From nazz:
prove; tan inverse 1/4=1/3 cot inverse 52/47
Answered by Chris Fisher.
A circle is inscribed in a hexagon 2015-12-28
From Lalitesh:
A circle is inscribed in a regular hexagon ABCDEF
Prove that AB+CD+EF=BC+DE+FA

Answered by Penny Nom.
A tangent line to a parabola 2015-12-02
From pei:
Given that the line y=mx-5 is a tangent to the curve y=2x^2+3 find the positive value of M.
Answered by Penny Nom.
A common tangent to two general parabolas 2015-11-15
From Kind:
Hi, I want to find the common tangent of two general parabolas, but i don't know if it's possible or not.
If it's possible, please make a tutorial.

The first parabola equation : Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.
The second parabola equation : Gx^2 + Hxy + Iy^2 + Jx + Ky + L = 0.

I need this because i want to find the equation of Beloch fold. (Huzita - Hatori 6th axiom) However if you know any other method to find Beloch folds equation, I am open for any suggestions.

Answered by Chris Fisher.
A tangent line to a circle 2015-09-03
From Jamie:
Use the Greek method to find an equation of the tangent line to the circle x^2+y^2-4x+6y+4=0 at the points (3,2square root 2-3.
Answered by Penny Nom.
A tangent to y = x^3 2015-05-31
From Brayden:
Show that a tangent line drawn to the curve y=x^3 at the point (d,f (d)), where d>0, forms a right triangle with the x and y axes in quadrant 4 whose area is (2/3)d^4.
Answered by Penny Nom.
A circle is tangent to the y-axis 2015-05-06
From Elynna:
What does it mean when a circle is tangent to the y-axis?

Thanks,

Answered by Penny Nom.
Two concentric circles 2015-04-21
From Juniper:
Two concentric circles have radii of 4 cm and 8 cm. A segment is drawn so that it is tangent to the smaller circle and a chord of the larger circle. How long is the segment?
Answered by Penny Nom.
A tangent to y=x^3 passes through (0,2) 2015-04-05
From Kevin:
Given that the curve y=x^3 has a tangent line that passes through point (0,2). Find the equation of the tangent line
Answered by Penny Nom.
Two parallel tangents to a circle 2015-03-05
From Samantha:
The equation of a circle is x^2+y^2=25. Determine the equation of the parallel tangent lines to this circle, for which the slope is 4/3.
Answered by Penny Nom.
A tangent to a circle 2014-12-22
From azman:
Find the equation of the tangent line to the circle x^2+y^2=9 at the point P (2, square root of 5).
Answered by Penny Nom.
A tangent to a curve passing through a point not on the graph 2014-09-15
From Aquilah:
For the curve y = x2 + 3x, find the equations of all tangent lines for this graph that also go through the point (3, 14).
Answered by Penny Nom.
A tangent of the curve (x/a)^n+(y/b)^n =2 2014-04-15
From sudhir:
the equation of tangent of the curve (x/a)^n+(y/b)^n =2. at(a,b) is
Answered by Penny Nom.
Two circles that touch each other externally 2014-04-08
From Ameya:
Two circles of radii a and b (a > b) touch each other externally. ST is a common tangent touching the circles at S and T respectively, then ST^2 is equal to
Answered by Chris Fisher.
A circle which is tangent to two perpendicular lines 2014-03-09
From MJ:
I'm a College Student taking up Bachelor of Secondary Education on Math Subject. And I'm struggling for my research about Circles. I done solving the said topic particularly on this question:

"What are the possible equations of a circle being tangent to a pair of perpendicular lines, having the origin as the Point of Intersection and the C (h, k), where h, k ∈ℤ"

But I can't get what would be the process that I must do in order to jive to my idea/goal for that problem.
Please check my idea that the numerical coefficients of the equation is equal to the radius of the circle. Thanks in advance! :)

Answered by Penny Nom.
Four tangent circles 2013-10-09
From Nilesh:
Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. How to find the area of the space enclosed by the four pieces?
Please let me know.

Answered by Robert Dawson.
Equal ordinate and abscissa 2013-08-15
From sonit:
the slope of tangent to the curve y=(4-x^2)^1/2 at the point, where the ordinate and abscissa are equal, is
Answered by Penny Nom.
A triangle and an incircle 2013-05-09
From Max:
On my Geometry Test about tangent, chord, and secant lengths, my teacher gave an extremely difficult problem.
It was a Circle inscribed in a Triangle with all triangle sides being tangents and lengths were given. My class was told to find the length of each segment of the line. The points on each line were the vertexes of the triangle, and the point where the line hits the circle.
Please explain how someone could do this.

Answered by Chris Fisher.
Tangents to the curve y = x^3 2013-03-24
From Ethan:
How many tangent lines to the curve y = x^33 pass through the point (2, 4)? For each such line, and the exact coordinates of the point of tangency on the curve.
Answered by Penny Nom.
Trigonometry 2013-03-23
From Tizoc:
I am in a trig class and I have a conflict. When solving the length of a side, I know what trig function to use, but I do not know what angle to use in a calculator. To make this a little more understandable, if I have all the angles available in a right triangle and I use the tangent function, how do I know what to use?
Heres what I do not know what to put in my calculator: Tan(?)
Thanks in Advance!

Answered by Penny Nom.
The tangent to a circle at a point on the circle 2013-02-22
From Andrew:
What is the equation of the line tangent to the circle with equation x^2+y^2=25 at the point (-4,3)
Answered by Penny Nom.
Four tangent circles 2012-10-04
From renu:
inside of a circle K of radius length measure R,three circular discs A,Band C each of radius r are placed so that each touches the other two and K . express R in terms of r. in the space between K, A and B , another circular disc D is placed which just touches K, A and B. if the radius is s, show that (6+root3)s=(2+root3)r
Answered by Penny Nom.
A tangent to f(x) = 1/x 2012-09-04
From Steven:
Consider the graph of the function f(x) = 1/x in the first quadrant, and a line tangent to f at a point P where x = k. Find the slop of the line tangent to f at x = k in terms of k and write an equation for the tangent line l in terms of k.
Answered by Penny Nom.
A tangent line to a circle 2012-04-14
From Novelyn:
find an equation of the line tangent to a circle with equation x^2+y^2+6x-8y-27=0 at the point P(1,-2)
Answered by Penny Nom.
Tangent of theta 2012-01-17
From stahl:
explain what the 'tangent of theta' means. Draw and label a diagram to help with your explanation.
Answered by Harley Weston.
An equilateral triangle and some circles 2012-01-10
From tushar:
draw an equilateral triangle with side 6cm.draw 3circles with radii 3cm on each angular point of triangle.draw common tangent on each of two circles
Answered by Penny Nom.
Lines tangent to y^2=4x 2011-11-11
From Reuchen:
Find equations of the lines tangent to y^2=4x and containing (-2,1).
Answered by Penny Nom.
One central circle and three tangent circles 2011-10-16
From Margaret:
You have one central circle and three or more circles tangent to the outside of the circle of varying radii. You know the x,y coordinates of the centers of the other circles. If you now remove that central circle (and pretend you never knew where it was), can you calculate its center in x,y coordinates?
Answered by Chris Fisher.
A tangent to the earth 2011-09-03
From Vickram:
I have a math problem regarding tangent and circle. My example is as follows: if a long flat ruler measuring 1500 miles is placed on top of earth which has a radius of 3960 miles what part (length) of the tangential ruler will actually be touching the earth and what two parts will not?
Answered by Chris Fisher.
Three tangent circles 2011-08-21
From maribie:
three discs are tangent externally distances between their centers are 23cm, 15cm, and 20cm. find their radii.t
Answered by Penny Nom.
Three tangent circles 2011-08-19
From hanniel:
two coin are tangent to a third coin internally and are tangent to each other externally. The distance between their centers are 14 mm, 17mm, and 5mm. find their radii
Answered by Penny Nom.
A line tangent to f(x)=1/x 2011-06-05
From Michael:
A line tangent to f(x)=1/x in the first quadrant creates a right triangle with legs the x-axis and the y-axis. Prove that this triangle is always 2 square units regardless of where the point of tangency is.
Answered by Penny Nom.
Three tangent circles 2011-05-01
From mark:
Three circles of radii 24 cm, 32 cm, and 42 cm are externally tangent to each other (each is tangent to the other two). Draw a diagram and using the Law of Cosines find the largest angle of the triangle formed by joining their centres.
Answered by Penny Nom.
A family of circles 2011-03-01
From steffi:
Find the equation of the family of the circle passing through the the point of intersection of x^2+ y^2 -4x-28=0 and x^2 +y^2 -4x-20+52=0; the member tangent to x=7.
Answered by Penny Nom.
Two tangent circles 2011-02-09
From xhesika(jessica):
Two circles of radius 10 are tangent to each other.A tangent is drawn from the centre of one of the circles to the second circle.To the nearest integer find the area of the shaded region.
Answered by Penny Nom.
A tangent to a circle 2011-02-06
From debz:
what is the formulae of the tangent to a circle.... our teacher gave us a lot of homework.. and she ask us to find the formulae by ourselves..
Answered by Penny Nom.
Tan(x+pi)-tan(pi-x)=2tan(x). 2011-01-09
From Steven:
Verify the identity:
Tan(x+pi)-tan(pi-x)=2tan(x)

Answered by Penny Nom.
A tangent line 2011-01-03
From Amanda:

Question from Amanda, a student:

an equation of the line tangent to y=x^3+3x^2+2 at its point of inflection is
(A) y=-6x-6
(B) y= -3x+1
(C) y= 2x+10
(D) y=3x-1
(E) y=4x+1


Answered by Penny Nom.
The equation of a circle 2010-05-04
From crystal:
find the standard form of the circle with center (-2,3) and tangent to the line y=1
Answered by Penny Nom.
A tangent line to a circle 2010-04-15
From Rhonda:
The Greek method for finding the equation of the tangent line to a circle used the fact that at any point on a circle the line containing the reauis and the tangent line are perpendicular. Use this method to find an equation of the tangent line to the circle x^2+y^2=9 at the point (1,2 square root of 2).
Answered by Penny Nom.
The equation of a circle 2010-02-18
From AHMED:
find the equation to the circle with centre at the point (1,-1) and touching the straight line 5x+12y=7.
Answered by Penny Nom.
Angle of incline 2010-01-20
From Alan:
how do I fnd the angle of an incline with a measurement of 0.042 with an adjacent of 1.2mtrs?. Thank You
Answered by Penny Nom.
A circle problem 2009-12-14
From Fawad:
AP is a tangent at P to a circle centre O, where AP=6cm. The straight line AQC is such that QC= 9cm. Find the length, in cm of AQ.
Answered by Chris Fisher.
f(x)=x+2sinx 2009-12-12
From amroziz:
for which values of x does the graph of f(x)=x+2sinx have horizontal tangent
Answered by Harley Weston.
The triangle formed by the tangent and the coordinates axes 2009-11-23
From Nirmala:
Given that y=1/x, x is not equal to zero. Prove that the area of the triangle formed by the tangent and the coordinates axes is 2.
Answered by Harley Weston.
Three circles 2009-10-02
From Brandon:
There is a quarter circle with a radius of 1. along one eged of it, there is a semi-circl with a diameter of 1, and its center is on the drawn line. there is another semi-circle again with the center on the other drawn line, and this one has an unknown diameter of X. both circles are internally tangent, and are tangent to each other. Find X.
Answered by Robert Dawson and Chris Fisher.
A line tangent to a parabola 2009-10-01
From kanchan:
for what value of c a line y=mx+c touches a parabola y^2=4a(x-a)
Answered by Penny Nom.
A tangent to a circle 2009-07-14
From Eric:
Hi I am trying to complete a packet that has a list of questions to brush up on pre-calculus skills. The question asks "For the circle x^2 +y^2 + 6x - 4y + 3 = 0 find : the equation of the tangent at (-2,5). I have already found the equation for the circle and standard form and the center and radius. However, i do not know how to find the slope or y-intercept of the tangent line. Please help. Thanks.
Answered by Stephen La Rocque.
4 tan(360/(2n)) 2009-05-18
From molly:
in the formula to find the area of any regular polygon how do you figure out 4tan part of the formula
Answered by Penny Nom.
A common tangent to two curves 2009-03-02
From Jay:
For what values of a and b will the parabola y = x^2 + ax + b be tangent to the curve y = x^3 at (1,1)?
Answered by Penny Nom.
A point on -8x^2+5xy+y^3=-149 2009-02-04
From Vivian:
Consider the curve defined by -8x2+5xy+y3=-149
a) find dy/dx
b) Write an equation for the line tangent to the curve at the point (4,-1)
c) There is a number k so that the point (4.2,k) is on the curve. Using the tangent line found in part b), approximate the value of k.
d) write an equation that can be solved to find the actual value of k so that the point (4.2,k) is on the curve
e) Solve the equation found in part d) for the value of k

Answered by Harley Weston.
Two tangent circles 2009-01-23
From Murtaza:
Two circles touch externally at T. A chord of the first circle XY is produced and touches the other at Z. The chord ZT of the second circle, when produced, cuts the first circle at W. Prove that angle XTW = angle YTZ.
Answered by Robert Dawson and Chris Fisher.
A cyclic quadrilateral 2009-01-23
From Murtaza:
Line ATB touches a circle at T and TC is a diameter. AC and BC cut the circle at D and E respectively.Prove that the quadrilateral ADEB is cyclic.
Answered by Robert Dawson and Chris Fisher.
1 foot drop every 25 feet 2009-01-22
From jerry:
1 foot drop every 25 feet what is the angle of the degree
Answered by Penny Nom.
Two tangent circles and common tangents 2008-12-01
From Alan:
Radius of big circle 30cm, radius of small circle 10 cm. From the diagram, the radius from the tangent do not form a semicircle but at an angle. Find the perimeter of the band around both the circle. May need to use trigonometry to find reflex angle AOB, CMD and get the major arc length AB and minor arc length CD
Answered by Penny.
Two tangents to a circle 2008-11-26
From rogerson:
The length of the tangent to a circle is 15 cm. If the angle between the two tangent lines to the circle is 28 degrees, what is the radius of the circle?
Answered by Penny Nom.
Tan(3x) 2008-11-23
From Evan:
Derive an expression for tan3x in terms of tanx
Answered by Harley Weston.
A circle tangent to a line and with its centre on another line 2008-11-01
From liza:
Find the equation of the circle of radius squareroot 26 tangent to the line 5x+y=13 and having its center on the line 3x+y+7=0.
Answered by Chris Fisher.
Tangent line 2008-10-27
From Maddie:
Find a general equation for a line that touches, but does not pass through the function Y=X2(X squared) + BX+C.
Answered by Stephen La Rocque and Victoria West.
Two tangent lines to a parabola 2008-10-26
From Marcus:
Show that the tangent lines to the parabola y = ax^2 + bx + c at any two points with x-coordinates p and q must intersect at a point whose x-coordinate is halfway between p and q.
Answered by Penny Nom.
The slope of a tangent line 2008-10-18
From Amanda:
If f(x)=square root of (x+4), and the slope of the tangent line at x=21 was 1/n for some integer n, then what would you expect n to be?
Answered by Stephen La Rocque.
A tangent line to f(x) = 1/(x - 1) 2008-10-16
From Amanda:
If f(x)=1/(x-1) then what is the slope of the tangent line at x=-2?
Answered by Harley Weston.
How many parallel tangents may a circle have? 2008-09-29
From Manish:
how many parallel tangents may a circle have? the text book shows two.but a circle can have infinite tangents.then why not parallel tangents coz theoretically each tangent have a parallel tangnts then no. of parallel tangent a circle may have is equals to half of the infinity i.e. infinity..
Answered by Walter Whiteley.
Parallel Tangents 2008-09-24
From manish:
how many parallel tangents may a circle have? the text book shows two.but a crcle can have infinite tangents.
Answered by Janice Cotcher.
A tangent to a circle 2008-09-06
From Jake:
Find an equation of the line that is tangent to the circle x^2 + y^2 = 3 at the point (1,√2)
Answered by Penny Nom.
Two tangent circles 2008-08-22
From Michele:
A circle of radius 2 is externally tangent to a circle of radius 8, How do you find the length of their common tangent.
Answered by Penny Nom.
Irregular polygon and Circle that Intersects All Sides 2008-08-20
From Xetro:
Hi, Suppose you have an irregular polygon(convex or concave) with n > 3 sides. The question is - Find some circle that will cut(in limiting case - touch) all the sides of that polygon. It doesnt matter how many times it cuts the side(1 or 2), it just have to cut or touch it. How to find such a circle? or how to decide if such circle even exists? What if those segments do not form a polygon but are some arbitrary segments ? Really want to know how to do it................ Thanks a lot.. Regards, Xetro
Answered by Janice Cotcher.
Area of triangle formed by three tangent circles 2008-07-31
From brian:
Three circles with radii 3,4 and 5 touch each other. The circles are tangent to each other. What is the area of the triangle formed by the centers of the circles?
Answered by Stephen La Rocque.
A tangent to a curve through a point not on the curve 2008-07-23
From Carter:
How does one find the tangent points on a curve, given only the curve's function and the x-intercept of that tangent line?
i.e. Find the point(s) on the curve y = -(x^2) + 1, where the tangent line passes through the point (2, 0). I know that there will be two such points, one where y is very close to 1, and the other point where y is a large negative number. However, I do not recall how to figure out the tangent line equation given a single intercept and solving to find the tangent points.

Answered by Penny Nom.
A tangent line to a circle 2008-07-09
From Rita:
The tangent to a circle may be defined as the line that intersects the circle in a single point, called the point of tangency. If the equation of the circle is x^2 + y^2 = r^2 and the equation of the tangent line is y = mx + b, show

r^2(1 + m^2) = b^2

Answered by Harley Weston.
A space camera circles the Earth 2008-06-16
From Rita:
A space camera circles the Earth at a height of h miles above the surface. Suppose that d distance, IN MILES, on the surface of the Earth can be seen from the camera.

(a) Find an equation that relates the central angle theta to the height h.

(b) Find an equation that relates the observable distance d and theta.

(c) Find an equation that relates d and h.

(d) If d is to be 3500 miles, how high must the camera orbit above Earth?

(e) If the camera orbits at a height of 400 miles, what distance d on the surface can be seen?

Answered by Penny Nom.
tan(4a - b) 2008-06-12
From A student:
hi guys just a quick help on question needed thanx if tan a = 1/5 and tan b = 1/239 find value of tan(4a-b) thanks alot in advance
Answered by Harley Weston.
Three mutually tangent circles 2008-06-04
From Jacob:
If three circles are mutually tangent, does that mean that the two tangent lines are perpendicular?
Answered by Chris Fisher.
How many bricks I can place around a 26-inch circle? 2008-05-22
From Jon:
I want to know how many bricks I can place around a 26-inch circle? There must be a formula other than trial and error. The length of the bricks is 6-inches. [How many 6-inch tangents can be in a 26-inch circle? Thank you very much. Jon
Answered by Harley Weston.
A tangent to two circles 2008-04-13
From erson:
find the length of the tangent segment AB to two circles whose radii are a and b respectively, when the circles touch each other.

the illustration looks like this...hope you'll understand... there are 2 circles - one is big one is small. they touch each other. and there is this irregular 4 sided polygon that connects them...there is a line that connects them from their center point and another from the tip of the circles...and that's it...i cannot explain very well please bear with me

Answered by Stephen La Rocque.
A tangent to a circle 2008-04-13
From rogerson:
Line t from point P is tangent to circle O at T, the point of tangency. Find the length of PT when the radius of the circle is 5cm and the distance between points P and O is 8cm.
Answered by Stephen La Rocque.
The equation of a circle 2008-02-05
From aime:
Find the equation of the circle tangent to 3x+4y-15=0 at P1(1,3) and passing through P2(6,3) and P3(0,5)?
Answered by Stephen La Rocque.
A tangent to a circle 2008-01-04
From adam:
Find a>0 so that the line y=x+a is a tangent to the circle x^2 +y^2=2.
Answered by Stephen La Rocque and Harley Weston.
Lining up coins visually using geometry and trigonometry 2007-12-31
From Jessica:
a) In what order would you arrange a penny, a nickel, a dime, a quarter, and a half-dollar so that they all have the same apparent size? The diameters of the coins, in thousandths of inches, are as follows: penny, 750; nickel, 835; dime, 705; quarter, 955; half-dollar, 1205.
b) How should the coins be placed, if the distance between the dime and the half-dollar is 100 units? How far from thw dime should your eye be to see that all the coins have the same apparent size?
c) What angle do the coins subtend when they have the same apparent size?

Answered by Stephen La Rocque.
The tangent to a curve 2007-12-10
From Christy:
I know this question is simple but I can't figure out what I'm doing wrong.
Find the equation of the tangent line to the curve 2x^2 - y^4= 1 at the point (1,1).

Answered by Penny Nom.
A triangle and a pentagon 2007-12-08
From Olivia:
A regular pentagon has an area of 800 square centimetres. What is the area of the triangle extended from one side of the pentagon?
Answered by Stephen La Rocque.
A particle moves in the xy-plane 2007-11-12
From Russell:
A particle moves in the xy-plane with

X = 2t^3 - 12t^2 + 18t

Y = 3t^4 - 28t^3 + 72t^2

find an equation of the line tangent to the given curve at t_0_ = 1

note: t_0_ is t subscript 0

Answered by Harley Weston.
Equation of a tangent line to a function 2007-10-04
From Princess:
If f ' (x) = 3x^2 +1, find the equation of the tangent line to f(x) = x^3 + x at x= -1.
Answered by Stephen La Rocque.
A tangent line to a circle 2007-09-26
From Randy:
Find the equation of the tangent line at coordinates (-1 , 4) on the circle x^2 + y^2 - 4x - 21 = 0

I would like to learn the fastest way to relate any coordinates of a circle to any possible point of tangency.

Answered by Stephen La Rocque.
The tangent to y = x^3 at x = 0 2007-09-04
From Amit:
consider the equation = x^3. The equation of tangent to this curve (which is smmetrical in Ist and IVth quadrant) at (0,0) is y=0, which is x-axis. but graphically one can visulize that x-axis intersects the curve, so how can it be the tangent to the curve. Please help.
Answered by Harley Weston.
A circle and a tangent 2007-08-27
From Lindsay:
Hello. I'm trying to do a math problem and have searched the internet for equations but have come up empty handed. If you could help, that would be greatly appreciated! The problem is stated thus: A circle is tangent to the y-axis at y=3 and has one x-intercept at x=1.
a. Determine the other x-intercept
b. deduce the equation of the circle.

Answered by Penny Nom.
Two-column proof for a circle geometry problem 2007-08-24
From Kendra:
i have to prove that tangents to a circle at the endpoints of a diatmeter are parallel by stating whats given, whats to prove and a plane, then write a two column proof i dont understand this
Answered by Stephen La Rocque.
Tangents to a circle 2007-08-18
From Laura:
I have tangents from point A and B that intersect at C. A third tangent XY lies in between the two lines that I have already drawn. I measured the perimeter and then I drew another line that was tangent to the circle and was inside the two lines again and measured the perimeter again. The perimeters were the same but I don't know how to prove why this happened and write a theorem for it.
Answered by Chris Fisher.
Two circles C1 and C2 meet at the points A and B 2007-08-15
From Jerry:
Two circles C1 and C2 meet at the points A and B. The tangent to C1 at A meets C2 at P. Point Q inside C1 lies on the circumference of C2. When produced, BQ meets C1 at S and PA produced at T. Prove that AS is parallel to PQ.
Answered by Chris Fisher.
Circle Geometry 2007-08-14
From Robin:
In a triangle ABC, angle A=75 and B=60. A circle circumscribes the triangle. The tangents of the at points A and B meet in a point D outside the circle. Show that ABD is an isosceles triangle with a right angle at D. Diagram included.
Answered by Stephen La Rocque.
Diagonals on a cylinder 2007-08-10
From John:
I have a cylinder that is 37.5" width X 25.25" circumference. I need to create a repeating diagonal lined pattern on the cylinder so that when it prints it joins perfectly at the circumference repeat. The design must follow these specs. Black diagonal lines need to be 1.250" max width X 1.5" max spacing between the black lines. Please Help
Answered by Stephen La Rocque.
Two tangent lines to y=x^3 2007-06-07
From stephanie:
find the equations of two tangent lines to the y=x^3 function through the point (2,8)
Answered by Penny Nom.
Finding the hypotenuse without Pythagorus 2007-05-11
From Shelbie:
How do i find the hypotenuse of a right traingle not using the pythagorean thereom if i have the measurements of the legs?
Answered by Stephen La Rocque.
Two tangents to a circle 2007-04-17
From Doug:
Two distinct, nonparallel lines are tangen to a circle. The measurement of the angle between the two lines is 54 degrees (angle QVP). Suppose the diameter of the circle is 2 cm. What is the distance VP? Suppose the distance VP is 3.93 cm. What is the diameter of the circle? Find a formula for d, the diameter of the circle, in terms of VP. Find a formula for VP in terms of d, the diameter of the circle.
Answered by Stephen La Rocque.
The angles in a right triangle 2007-03-28
From Golaan:
I need the to understand the formula for finding either of the acute angles of a right triangle given it's hieght length and base length. I want to find the degrees of either accute angle. So for this example I have a right triangle with a height of 410 meters and a base length of 1,700 meters. I don't understand cosine, sine, and tangent or the other ones at all. So if the solution includes those (which I believe it does) could b very verbose yet in a very elementary way?

The purpose of ths is that I have to define the general incline angles (or grade) of various areas of terrain. I know the distance by map and also the the altitude at either endpoint.

Answered by Penny Nom.
Triple angle tangent formula 2007-03-15
From sam:
Hi I am trying to derive a triple angle formulae for tan. I know i need to use compound and double angle formulae but am finding it difficult to "clean" up my fraction to get the triple angle formulae can you show me a worked derivation?! thanks
Answered by Penny Nom.
Angle of elevation 2007-03-13
From Joslyn:
A ship at sea sights a 12m high lighthouse on a cliff which is 80m above sea level. If the angle of elevation to the top of the lighthouse is 27 degrees, calculate the distance from the ship to the shore.
Answered by Haley Ess.
Finding the equation of the circle 2007-02-20
From ning:
Given the radius of a circle square root of 10 tangent to the line 3x+y+19 = 0 and passing through (0,-3), how can i solve the equation of circle? thank you...
Answered by Chris Fisher, Steve La Rocque and Penny Nom.
A common tangent line 2007-02-20
From chris:
I have this problem I have been working on for days and cannot figure it out. it states: Find the two points on the curve y=x^4 - 2x^2 - x that have a common tangent line.

I know you use the first derivative to find the tangent line so if it is a common tangent line should you find two of the exact same tangent line equations at two coordinate points?

Answered by Chris Fisher.
Circle geometry 2006-11-19
From Namrata:
AB is a diameter and AC IS A CHORD OF A CIRCLE SUCH THAT angle=30. the tangent at C intersect AB produced in a pointD. Prove that BC=BD.
Answered by Stephen La Rocque.
Tangent lines 2006-11-09
From Melissa:
let f be a function with f(1)=4 such that for all points (x,y) on the graph of f the slope is given by (3x^(2)+1)/(2y)

a.)Find the slope of the graph of f at the point where x=1.
b.)Write an equation for the line tangent to the graph of f at x=1 and use it to approximate f(1.2)
c.) Find whether f is concave up or concave down when x=1. Is your answer in part b an overestimate or an underestimate?

Answered by Stephen La Rocque.
How high (in feet) is the mountain? 2006-08-29
From Briana:
A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 29 degrees. From a point 2000 feet closer to the mountain along the plain, they find that the angle of elevation is 31 degrees. How high (in feet) is the mountain?
Answered by Stephen La Rocque.
A tangent to a circle 2006-07-05
From Izumi:

I have problems finding the point of tangency between the circle C

x2 + y2 + 4x - 6y - 12 = 0

and the tangential line that passes through the point P (6, -1).


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.
Geometry proof 2006-04-23
From Jade:
From a point P outside a circle with centre O, tangents are drawn to meet the circle at A and B. a) Prove that PO is the right bisector of the chord AB. b) Prove that
Answered by Stephen La Rocque.
Two circles 2006-04-07
From Louisa:
One circle of radius 7cm is touching another circle of radius 4cm. These circles are on a line and the problem is to find the length AB where A is the point marking the bottom of the radius of one circle and B is the point marking the bottom of the radius of the other circle.
Answered by Stephen La Rocque.
A sequence of circles and tangents 2006-01-16
From Paul:
Consider a circle whose center is (2,2) and whose radius is 1, and the straight line that goes through the origin and that is tangent to this circle so that the intersection between them is as shown in the attached picture. With this new point we make a new circle whose radius is half of the first one, and we calculate the corresponding intersection point with the same suppositions as in the first case. We repeat the process to the infinite. Find the distance between the center of the circle in the infinite and the origin (point (0,0)).
Answered by Chris Fisher.
Four tangent circles 2005-12-06
From Ananth:

I have one bigger circle A with radius 15.

Inside this bigger circle i have another circle B with radius 3 which touch this bigger circle. Have another circle C with radius 4 which touches A and B. I would like to draw a biggest circle which touches A,B and C.


Answered by Chris Fisher.
A tangent to a parabola 2005-11-02
From A student:
Find the point on the curve y=x2 where the tangent to the curve is parallel to the secant line connecting (-1,1) and (2,4)
Answered by Penny Nom.
Two tangents to a circle 2005-06-18
From Tej:
The tangents drawn from points M and N of a circle having centre O intersect each other at point P. If angle MPN=60 degrees, NM=10, then find the radius of the circle and Area of quadrilateral OMPN.
Answered by Penny Nom.
Tangents to a circle 2005-03-19
From Sue:

You're given the equation to a circle (x-3)2 + (y-3)2 = 4 and you need to do 3 things:
1. Find a point on the circle
2. Construct an equation for a tangent line to the circle and through the point
3. Plot the circle, point and the tangent line on one graph

Answered by Penny Nom.
Three tangent circles 2005-01-25
From Kate:
Two circles, C1 and C2, touch each other externally; and the line l is a common tangent. The line m is parallel to l and touches the two circls C1 and C3. The three circles are mutually tangent. If the radius of C2 is 9 and if the radius of C3 is 4, what is the radius of C1?
Answered by Chris Fisher.
The tangent line at an inflection point 2004-11-28
From Louise:
the equation of the tangent line to the curve y = x3 - 6x2 at its point of inflection is...
Answered by Penny Nom.
A common tangent line 2004-10-05
From Shanup:
The x-axis is a common tangent of y = x^2 and y = x^3. Find the equation of another common tangent.
Answered by Penny Nom.
A tangent to a hyperbola 2004-08-02
From A student:
The equation of a hyperbola is 32x*2 -18Y*2-64x +72y +248=0. The equation of a tangent line to this hyperbola is y= (16/15)X + 10/3 I have been trying to find the point where this line intersects the graph. What I did was solve for x and then plugged in the result into the equation of the hyperbola, but I am getting two answers and I am supposed to get only one because the line is tangent to the graph. For this reason, I would like to know what I am doing wrong or what I have to do to know which answer is correct.
Answered by Penny Nom.
The tangent of theta 2004-07-10
From Jacob:
P is a point on a unit circle with coordinates(0.6,0.8). Find tan of theta. My book shows me how to do it,"tan of theta=opp./adj.=0.8/0.6=4/3,"and leaves it as that's the answer(4/3).When do we know from a problem to find the angle measure (in this case, the angle measure of theta) and how do we know when to give something like 4/3 without converting it to the angle measure?
Answered by Penny Nom.
A tangent to a quadratic 2004-06-04
From Jem:
I have a question on the tangent to a quadratic curve. Say I have a curve y = ax2 + bx + c. The gradient, using the derivative of y, at any point x on the curve is: 2ax + b right? Then, for the tangent that cuts the curve at a point x, the equation of the tangent can be: y1 = (2ax + b)x1 + d.

My question is, how is the point d of this tangent determined? It is the point on the y-axis where the tangent cuts isn't it? Is there a formula for it?

Answered by Penny Nom.
The center of a circle 2004-05-26
From Wan:
I am trying to find the radius of an arc. The only things i know about the arc is all referenced from the line of tangency to the arc. on both sides i have a differnt horizontal perpendicular distance to the point of tangency. left side |-------*---------------| right side (*=point of tangency). Then i have 2 difference vertical perpendicular distance of the end points to the line of tangency. I know it sounds very bad in text but this is all i know about the arc. Can you help me find the radius?
Answered by Penny Nom.
A geometry problem 2004-03-04
From Jennifer:
I need help with this problem: Square ABCD has side length 2. A semicircle with diameter AB is constructed inside the square, and the tangent to the semicircle from C intersects side AD at E. What is the exact length of CE?o
Answered by Chris Fisher.
The sketch of a graph 2003-10-07
From A student:
I was wondering how do you figure out if a graph has a horizontal tangent line. One of my homework problem was to sketch the graph of the following function; (4/3)x3-2x2+x. I set f''(x) ( the second derivative) of the function equal to zero and got the inflection point:(1/2,1/6). Also i am having trouble finding the concavity for x>1/2 and x<1/2, i am getting a different answer from the back of the book, the graph i draw looks completely different from the correct answer.
Answered by Penny Nom.
The slope of a tangent 2003-10-01
From A student:

find the slope of the tangent to each curve at the given point

f(x)=square root 16-x, where y=5


Answered by Penny Nom.
A theorem in geometry 2003-09-02
From Diego:
Please refer to figure in attached file. P is a point on the chord AB of a circle such that the tangent PT which touches the circle at T is equal to AB. How do we prove that PT2 = AP x BP.
Answered by Dieter Ruoff and 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.
A circle, tangent to two circles and a line 2003-04-30
From Keith:
I have a horizontal line (that is treated as a datum line or the X axis), with two circles having their center points at different heights from that line (X1,Y1 & X2,Y2). The two circles are also at different diameters (R1 & R2). Both circles and the line (X-Axis) do not intersect nor are they tangent. My goal is to determine the maximum diameter of an inscribed circle that will fit between all three.
Answered by Chris Fisher and Harley Weston.
A tangent to a circle 2003-04-18
From Lech:
The line with equation y=mx is a tangent to the circle with equation x2+y2-6x-6y+17=0. Find the possible values of m.
Answered by Harley Weston.
Trigonometry problems 2002-12-01
From Chiara:
  1. Find tan 35pi/4
  2. Graph y = cos2x - 2sinx

Answered by Penny Nom.
Constructing a tangent to two circles 2002-11-28
From Tom:
I have two circles, different sizes a known distance from each other. We know the radii of the circles. How do I construct a line that is tangent to both circles relative to the segment that connects the centers of both circles?
Answered by Chris Fisher and Penny Nom.
The tangent to a curve and the tangent of an angle 2002-08-26
From A teacher:
Is there a relationship between the tangent of a curve(line touching the curve at one point) and tangent (the trigonometric function)?
Answered by Chris Fisher.
The slope of a tangent line 2002-03-04
From Ridley:
Suppose a function f(x) has the line 3x+4y=2 as its tangent line at x=5. Find f'(5).
Answered by Harley Weston.
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 tangent line 2001-11-21
From A student:
write an equation of the line tangent to the graph of

ey + ln(xy) = 1 + e at (e,1)

Answered by Harley Weston.
A trig identity 2001-07-27
From Jeff:
prove this identity and show steps
tan(x/2+pi/4)=secx+tanx

Answered by Harley Weston.
Three tangents to a circle 2001-06-27
From Stephanie:
The three lines PS, PT, and RQ are tangents to the circle. The points S, X, and T are the three points of tangency. Prove that the perimeter of triangle PQR is equal to 2PT.
Answered by Chris Fisher.
The normal to a curve 2001-04-08
From Varenne:
I am having SO much trouble tackling this question and don't know what the right answer is... can you help me out? The question is

Find the equation of the normal to the curve y=(x-2)2/(1-x)2 that is parallel to the line x+4y+7=0

Answered by Harley Weston.
Common tangents 2001-04-08
From Anne:
I have been working on this problem for a while but I'm not sure I'm getting the right answer: Find the common tangents of 2y=x2 and 2y=-x2-16 Thanks for the help. :)
Answered by Harley Weston`.
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 angle of elevation 2001-03-08
From Jeffrey:
At a Certain time, a vertical pole 3m tall cast a 4m shadow. What is the angle of elevation of the sun?
Answered by Harley Weston.
cot(arcsin 3/5) 2001-01-07
From Jason:
Find value. Assume that all angles are in Quadrant 1.

cot(arcsin 3/5)


Answered by Harley Weston.
Triangles and trigonometry 2000-11-30
From Mose:
If I have a right triangle, and I know the lengths of all three sides, is there a formula that will allow me to determine the measurements of the 2 non right angles?
Answered by Harley Weston.
A trig question 2000-07-01
From Will:
An open rectangular tank a units deep and b units wide holds water and is tilted so that the base BC makes an angle theta with the horizontal. When BC is returned to the horizontal, who that the depth of the water is

(a squared) * cot theta div 2b units


Answered by Harley Weston.
Parallel tangents 2000-06-30
From Ebony Indalecio:
I need to prove the theroem: Tangents to a circle at the end points of a diameter are parallel.
Answered by Walter Whiteley.
A parabola problem 2000-03-23
From Morin:
I need to prove that if parabola x2=4py has a chord (not necessarily a focal chord) intersecting it at points A and B, with tangents to the parabola at points A and B that intersect at C, then a line drawn through C and the midpoint of the chord M is parallel to the y-axis. Further, prove that the point D where this line intersects the parabola is the midpoint of line CM.
Answered by Penny Nom.
Angle of Intersection of Two Lines 2000-03-02
From Veronica Patterson:
I am having a real hard time trying to figure out this problem. Could you please help me! The homework question says to find the acute angle of intersection between the two lines y=3x+1 and y=(1/2)x-1. (It also says to use the results of a problem I had already figured out.) That problem was to use information from a picture shown that tan(theta sub1-theta sub2)= ((m sub2- m sub1)/(1+(m sub1 * m sub2))). I used the difference identity of tangent to figure out the answer. Any help on this problem would be greatly appreciated.
Answered by Harley Weston.
Trigonometry history 1998-05-26
From Joeseph Huckler:
Can you please tell me some history of the trigonometric ratio Tangent? who discovered it? when was it discovered and some other useful info...
Answered by Penny Nom.
The Length of a Chord. 1997-07-26
From Nathan Arthur:
Picture a 9 inch diameter circle. Inside that circle is a 6 inch diameter circle tangent to it. Then, tangent to both circles is a 3 inch diameter circle. So there are three circles, two smaller ones inside a big one, all of them just touching but not overlapping.

Now picture a chord on the 9 inch circle that is created by making a line that is tangent to both the 6 and the 3 inch circles and extending it to the edge of the 9 inch circle.

I need the length of that cord.
Answered by Chris Fisher.

The angle between two tangents. 1997-06-09
From Felix Ho:
Two tangents are drawn from the origin to the circle (x)(x)+(y)(y)-4x-6y+9=0. If the angle between the tangents is m, fine the value of tan(m).

P.S. (x)(x)=square x
Answered by 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 tangent to a circle is perpendicular to the radius at the point of contact. 1996-10-22
From Rita Leung:
I wonder if there is any proof for this theorem - A tangent to a circle is perpendicular to the radius at the point of contact. If there is any proof for that, can you tell me please?
Answered by Chris Fisher and Harley Weston.
 
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