0
votes
0answers
22 views

Computing the coordinates of a point, offset from a rotated point.

Good day. I have a question which should be easy but I have not been able to figure it out. The coordinates of a point on a unit circle, given an angle, is $$\begin{align} x &= \cos(\alpha) \\ y ...
2
votes
2answers
30 views

Get the angle in a circle using center, radius and one point in a circle.

There is a circle and i know Point1 this is fixed and i know another point Point2 which can be anywhere in the circle. and i want to know the angle which is made at center. Thanks Your help will be ...
4
votes
3answers
71 views

what does tangent mean?

I need your help, my question is what does tangent value mean and how can we benefit from it ? I know that $\tan(\theta) = \dfrac{\sin(\theta)}{\cos(\theta)}$, but what does that mean? Sorry I am ...
2
votes
0answers
55 views

To find a fifth degree equation by using circles and lines that cannot be solved by radicals

An example quintic whose roots cannot be expressed by radicals is $x^5 - x + 1 = 0$. I asked a geometry question about a fifth degree equation long time ago . I had an equation in the question. It ...
3
votes
1answer
42 views

Find Area of 3 Sector Circle, Variable center point

I have a Circle separated into 3 sectors. At start each sector has the same central angle, 120°. Therefore each sector should be taking up the same area. I want to be able to move the center point ...
0
votes
3answers
58 views

Find how far runners travel on a circular track (trig)

-How far has each runner traveled after 8 seconds? Though I just had to convert the rad/sec to rev/sec to get yards then multiply that by 8 seconds, but that isnt correct. Find the angle θ, in ...
0
votes
1answer
35 views

Equation of tangent on Cartesian plane given center and radius of a circle

If I have a generic circle with radius $r$ and center $(h, k)$, and a tangent line with point of tangency $(x, y)$, can you give me the equation of the tangent line? Thanks!
-1
votes
0answers
56 views

Finding how far east of a starting point

George and Paula are running around a circular track. George starts at the westernmost point of the track, and Paula starts at the easternmost point. The illustration below shows their starting ...
1
vote
1answer
28 views

Find Coordinates on a track

Charlie and Alexandra are running around a circular track with radius 60 meters. Charlie started at the westernmost point of the track, and, at the same time, Alexandra started at the northernmost ...
0
votes
2answers
41 views

Finding coordinates on a circle

So this problem I am have difficulty with. I think where I am going wrong is how to calculate the initial theta. Do I just use pi/2 because in the pictures it show to angle theta off the 90 degree ...
1
vote
0answers
21 views

arrange div elements in circle and square

I n number of divs which are arranged in a circle using javascript. Right now i set the dimension of each div to 40*40. Below is what i am able to achieve so far. This is how i find X & Y of each ...
0
votes
0answers
16 views

How to compute an angle from arbitrary limits (min and max) and a default value?

My question is about a software problem but I think it's more related to Math equations. I'm developing a round knob which is limited to 315deg with a 45deg unused part of the knob. I have some ...
0
votes
1answer
43 views

How do I calculate the height of a cross section of a circle?

I'm working on an LED lighting project and have discovered that it involves a little math... I'm mounting LEDs to plexiglass facing away from the surface I want lighted. I'm looking at cutting a ...
3
votes
0answers
31 views

unit circle trigonometry where angles is greater than 90

how is possible to have sin of angle greater than 90. if sin is ratio of opposite side and hypotenuse in right angle triangle then triangle with one of the angle greater than 90 can not be right angle ...
0
votes
1answer
21 views

Simple algebraic question mixed up

I know it is very simple but do not know why I am mixed up in it $(.5)(r^2)\cfrac{20-2r}r$ how is this equal to $10r-r^2$ Sorry if it is too easy, thanks for the help.
0
votes
1answer
45 views

Finding the release angle for projectile

Hello. I would like to create an game application for android platform that is similar like projectiles. I called it snowball machine. As you know regular projectiles has to hit the ...
2
votes
2answers
81 views

Sine defined for a triangle inscribed in a circle with a diameter of one

Let a circle be drawn with a diameter of one (and thus a radius of one half). Then let a triangle with vertices A, B, and C be inscribed in the circle (i.e. points A, B, and C are arbitrary points on ...
2
votes
1answer
167 views

Arc Length from chord and tangent angle

This is for a rubberband-powered car competition. In the diagram above, I will be given the length from points A to B, as well as angle a. The car will need to go from A to B, positioned at a to ...
2
votes
1answer
81 views

Radius of circle by knowing a cross section.

I have a curve on an ellipse where I know the length of a cross section and need to find out it's radius (vertically and horizontally) and calculate the angle of the curve. In the following diagram ...
8
votes
3answers
267 views

How do you prove arc length is greater than chord length?

Graphically, it's obvious that given two different points $a$ and $b$ on a circle of radius $r$, the linear distance (chord length) from $a$ to $b$ is less than the arc length from $a$ to $b$. How do ...
1
vote
1answer
75 views

Radian and the length of a chord of a circle

Question In a circle of radius $r$, an arc of it is $2S$ long. Find the length of the chord corresponding to that arc (AB in the diagram below) . Details I got this question in a math test. And ...
1
vote
3answers
166 views

Find a circle's radius with three known tangent lines

I need to find the equation for a circle (mainly its radius) which is tangent to the following three lines: $y = 0$ $y = \tan(70)x$ $y = -1.428148x + 0.790201$ For the last tangent line equation, ...
2
votes
3answers
160 views

Find radius of a circle which is tangent to three known lines

I need to find the equation for a circle which is tangent to the following three lines: y=0 x=0 y=-x+0.338334 For the last tangent line equation, I know that it is tangent at the point (0.169167, ...
0
votes
1answer
30 views

How do I proof that $\angle ABP =\angle AP'B$ and that $P$, $Q$, $Q'$ and $P'$ are on 1 circle?

Given is a circle with center $M$ and a diameter $AB$. $k$ is the tangent to the circle at point $B$. On the circle there are two points called $P$ and $Q$, such that $P$ and $Q$ are both on the same ...
1
vote
1answer
70 views

Euclidean geometry: Circle incribed in a circle

Circle $c_2$ - with center $N$ - is inside circle $c_1$ and is tangent to circle $c_1$ - with center $M$ - in $P$. The line $l$ intersects $c_1$ at points $A$ and $D$ and $c_2$ at points $B$ and $C$. ...
1
vote
3answers
82 views

Circle equation with sine without parametric equation

I had to integrate an area delimited by a quarter of a circle, something like this: http://www.wolframalpha.com/input/?i=integrate+10+-+sqrt%2864+-+x%5E2%29+dx+from+0+to+5 Which comes from the ...
0
votes
1answer
97 views

how to find sin13° cos13° tan13° cot13° with trigonometric circle.

I have problem finding sin(13°) cos(13°) tan(13°) cot(13°)with trigonometric circle. I have to draw the circle with a triangle on it but I can't get the right thing.
1
vote
1answer
71 views

Derivation of the length of an arc formula

My textbook says that the radian measure of an angle is the ratio: $\theta = \frac{s}{r}$ Where s is a portion of the entire circumference, and r is the radius. So essentially the arc length is thus: ...
5
votes
1answer
202 views

How is the Radian measure of angles derived/defined? [duplicate]

I'm currently studying the foundation of trigonometry (angles and their measures) and I've just been told that $\pi$ is the ratio of a circle's circumference to its diameter, so: $\pi =\dfrac ...
0
votes
1answer
95 views

Given three points, find the arc length of a section between two intersecting lines.

I have three points, one being the center, and the other two are end points on a line drawn to the center. I need an equation that provides $\Theta$. In this drawing $(x_1, y_1)$ is the center.
1
vote
1answer
50 views

Unit circle - how to prevent backward rotation

Let's assume we have a unit circle (0, 2$\pi$). Basically I have a point on this circle who is supposed to move only forward. This point is controlled by the user mouse and constantly calculate 25 ...
4
votes
2answers
108 views

radius of circle inscribed in rectangle

I have two circles inside a rectangle(4 * 6), where the diameter of one of both is the total length of a side of the rectangle, and the other circle diameter is part of the length of the another side. ...
0
votes
1answer
36 views

Calculating the Apollonius Circle

This is a followup to a question I asked earlier. I have looked for an example on Google and StackExchange, but I have yet to see a clear example of the formula to determine the equation of an ...
3
votes
1answer
364 views

Solving circle's radius only knowing angle & lengths of external triangle OR solving for sides of a triangle partial side lengths

Is this possible? Given that I know the length of Y and Z and the angle of X can I figure out the radius A? If I can't without more information, I can produce another set of data X Y Z at a ...
3
votes
5answers
177 views

How do I find/predict the center of a circle while only seeing the outer edge?

Question What formula would allow me to predict the center of this circle? In addition, what attributes of this image must be detected in order to predict the center? I figured understanding the ...
10
votes
1answer
194 views

An Unexpected Circle…

I played around with $$z=\frac{-1+e^{it}}{\phantom{-}2+e^{it}}$$ and found that, when I draw the real against the imaginary of $z$, it pretty much looks like a circle. But neither ${\frak{R}} z ...
2
votes
1answer
57 views

Contract expression of circle segment area contingent on height

I want to determine a function for the area of the segment's height. I have made it this far, but I would like to contract the equation further - sadly, I do not know how to do this while still ...
0
votes
0answers
33 views

Finding the coordinates of the top and bottom circles of a moving and rotating cylinder in 3D

I have a cylinder that is moving and rotating in a 3D space. I need to calculate the coordinates of the center of the cylinder's top and bottom circles. Here's the information I have : I have at the ...
1
vote
0answers
143 views

Problems with Circles and Lines on a Cartesian Plane

(a) Find the equations of the two circles each of which touches both coordinate axes and passes through the point $(9,2)$. (b) Find the coordinates of the second point of intersection of the two ...
3
votes
4answers
12k views

How to find the equation of a line tangent a circle and a given point outside of the circle

I am given the equation of a circle: $(x + 2)^2 + (y + 7)^2 = 25$. The radius is $5$. Center of the circle: $(-2, -7)$. Two lines tangent to this circle pass through point $(4, -3)$, which is outside ...
2
votes
3answers
137 views

Simple circle geometry/ similarity question

How would you prove that a=b? Would i be possible to solve this using similarity or trigonometry? Thankyou in advance for any help. Any theorems or links would be appreciated
1
vote
1answer
302 views

If inside a big circle , exactly n $(n \geq 3)$ small circles, each of radius r,can be drawn in such a way that each small circle touches t…

Problem : If inside a big circle , exactly n $(n \geq 3)$ small circles, each of radius r,can be drawn in such a way that each small circle touches the big circle and also touches its adjacent small ...
3
votes
1answer
69 views

Let P be a moving point such that if $PA$ and $PB$ are two tangents drawn from $P$ to the circle $x^2+y^2=1 ( $ A ,B being the points of contact) ,…

Problem : Let $P$ be a moving point such that if $PA$ and $PB$ are two tangents drawn from $P$ to the circle $x^2+y^2=1$ ( $A$, $B$ being the points of contact) , then $\angle AOB = 60^{\circ}$, ...
1
vote
3answers
168 views

Equation of a Circle from parametric functions of sin and cos

Given: x = 2 cos (t/2) y = 2 sin (t/2) How do we find the equation of the circle? I know that x^2 + y^2 = 1, where x = cos(t) y = sin(t) so x^2 = (2 cos (t/2))^2 y^2 = (2 sin (t/2))^2 How do ...
2
votes
1answer
85 views

What am I doing wrong in this trigonometry/rate simulation problem?

I'm refreshing on some trig and cannot figure out how to solve this non-realistic word problem simulating a person walking in a circle. A person is located at the point (8,0) at time, t = 0, and ...
1
vote
1answer
46 views

Sectors of a Circle

I am programatically drawing sectors of a circle with radius 55 on a cartesian plane which runs from -55 to 55 on the x and y axes. I would like the first sector to be drawn at 0,55. I know I can ...
0
votes
2answers
46 views

Proof Error? A line-segment of a circle is a metric.

In O'searcoid, Metric Spaces, he provides the following example of a metric space: Suppose C is a circle and, for each $a,b ∈ C$, define $d(a,b)$ to be the distance along the line segment from $a$ ...
1
vote
1answer
167 views

Intersection of a point and absolute value function contained within a circle

I'm attempting some crazy ideas while programming a game and ran into the following math problem that has been bugging me for a few days: Given a unit circle and a random point $P$ within the circle, ...
1
vote
0answers
63 views

Is there a continuous version of $tan^{-1}(\frac{y}{x})$ for the entire unit circle?

The fact that $tan^{-1}(\frac{y}{x})$ only "works" for the upper-right quadrant makes some calculations (for a physics simulator) impossible. I of course use $atan2(y,x)$ in the code, that's not what ...
1
vote
1answer
96 views

$\pi$ is just a number, or also the circumference of a sub-unit circle?

A unit circle defined in the Cartesian plane has a radius of $1$ and a diameter of $2$. So making a full round is $2 \pi$. Now, $\pi$ is the ratio of the circumference over the diameter, so if I have ...