0
votes
1answer
17 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
33 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
48 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
88 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
0answers
65 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
219 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
58 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
97 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
106 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
28 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
64 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
70 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
92 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
54 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
153 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
73 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
46 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
80 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
35 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
159 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
123 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
191 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
52 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
29 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
132 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
9k 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
124 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
284 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
64 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
96 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
77 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
44 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
147 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
53 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
95 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 ...
1
vote
1answer
80 views

Circular motion trig

We have $x_P = -2 + 4 \cos (-\pi t)$ and $y_P = 1 + 4 \sin ( - \pi t)$ with $t$ in seconds. We have to find the coordinates of the intersection with the y-axis. So I use trig and I eventually end up ...
0
votes
1answer
125 views

How to find a point on the tangent line whos length is 1?

im trying to figure out a formula to find the point(x,y) on a tangent line whos length is between 0 and 1 while it rotates around the unit circle uniformly, so the point would either be right on the ...
0
votes
3answers
2k views

Calculating circle radius from two points and arc length

For a simulation I want to convert between different kind of set point profiles with one being set points based on steering angles and one being based on circle radius. I have 2 way points the ...
1
vote
1answer
75 views

Calculate points(x, y) within an arc

I am trying to draw lines from the center of a circle to points (x, y) in the circumference. To calculate this the angle is used. I need to render points in between two angles. E.g. Angle 0 to angle ...
1
vote
1answer
77 views

Calculating circle properties.

How can I incrementally calculate the angle from angle 0 and the point (x, y) in a circumference path if I have the center of the circle coordinates and the radius of the circle. I have 127 segments ...
1
vote
1answer
95 views

Calculating mean velocity of an orbiting body as it moves towards a point.

I'm making a game, in the game planets orbit a central point in circular orbits, they move directly towards their targets and the vector is simply added to their orbital path. Whilst not realistic it ...
0
votes
2answers
106 views

Question on inverse trig functions and quadrants? Please Help!

Alright, I was doing a question in a book, and it said: $\displaystyle \cos(2x - \frac{\pi}{6}) = \frac{\sqrt{3}}{2}$ I proceeded and got: $\displaystyle 2x - \frac{\pi}{6} = \frac{\sqrt{3}}{2}.$ I ...
2
votes
1answer
284 views

Finding side and angle of isosceles triangle inside two circles

I'm having a problem that I'm not sure how to solve (or if it's even possible). It's not homework, just something I'm struggling with for a project. :) Basically, there are two circles, represented ...
0
votes
1answer
44 views

How do you calculate the velocity of the pencil?

I'm drawing a quarter circle with a pencil on a sheet of graph paper. The radius is 10cm. At a given moment in time the velocity at which I am moving the pencil is 5cm/s (centimeters per second). I ...
0
votes
1answer
227 views

Given one endpoint on an arc of a circle and the radius and arc angle, how to calculate the other endpoint of the arc?

I have a circle with an arc beginning at point $(x,y)$. The radius is $r$, the arc angle(w/ respect to center) is $\theta$. How do I calculate the end point of the arc $(a,b)$ ? I know that the ...
12
votes
1answer
494 views

How does one calculate the product of $\tan 1^{\circ} … \tan 45^{\circ}?$

I have seen a question asked on yahoo asking to find the value of $\tan 1^{\circ} \cdot \tan 2^{\circ} \cdot \dots \cdot \tan 45^{\circ}$ (in degrees) I have seen various results concerning ...
3
votes
1answer
2k views

How to find an end point of an arc given another end point, radius, and arc direction?

Given an arbitrary arc, where you know the following values: end point (x1,y1), radius (r) and arc direction (e.g. clockwise or counterclockwise from start to end), how can I calculate the other ...
3
votes
1answer
79 views

Check If a point on a circle is left or right of a point

What is the best way to determine if a point on a circle is to the left or to the right of another point on that same circle?
2
votes
3answers
10k views

X and Y coordinates of circle giving a center, radius and angle

I have to find the necessary translations in X and Y to move a point 0n a circle to another one. I have a center (X and Y coordinates), a radius, and a current position in radians. And given a value ...