Tagged Questions
1
vote
1answer
73 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
20 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
63 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
2answers
120 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 ...
0
votes
0answers
27 views
Incorrect Points in Circumference
I am trying to calculate points in a circumference and I do not get expected values.
I am calculating it like this:
...
0
votes
1answer
22 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
35 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
59 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
52 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 ...
1
vote
0answers
119 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
38 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
45 views
Given one endpt on an arc of a circle and the radius and arc angle, how to calculate the other endpt 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 ...
13
votes
1answer
376 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
557 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
60 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?
1
vote
3answers
1k 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 ...
2
votes
2answers
180 views
Is the tangent function (like in trig) and tangent lines the same?
So, a 45 degree angle in the unit circle has a tan value of 1. Does that mean the slope of a tangent line from that point is also 1? Or is something different entirely?
4
votes
2answers
153 views
Find if a point is in a circle
I am coding a video game, but I am not so good at the math. I am hoping for some help here:
Given:
$X, Y$ that is the center of the Circle
$R$ that is the radius of the Circle
$X_1, Y_1$ that may ...
3
votes
1answer
131 views
Find the coordinates of a point on a circle
I have a circle like so
Given a rotation θ and a radius r, how do I find the coordinate (x,y)? Keep in mind, this rotation could be anywhere between 0 and 360 degrees.
For example, I have a ...
0
votes
1answer
44 views
What function could describe this situation on a Cartesian plane?
I have a problem as follows -
I have an arc, with a point on each end. And angle $a$ is how far the arc goes. I need to find the top right point ($P(w, x)$) in relation to the $r$, $P(x, y)$, and $a$ ...
1
vote
2answers
95 views
area of a circle - 3/4th
How to find the pixels of that line which is crossing the circle?
Is there any formula?
Iam getting the line's end points
2
votes
3answers
86 views
How do I rearrange this formula? Circles around a larger circle.
My A-Level algebra is failing me. Can someone please tell me how to rearrange this formula to give $n$ when you know $R$ and $r$.
$R \sin(180^\circ/n)/(1 - \sin(180^\circ/n)) = r$
This formula is ...
0
votes
3answers
160 views
How do I get the slope on a circle?
I have drawn a circle by doing this in Matlab: syms x;
ezplot(cos(x),sin(x))
I get the tangent point at which I want my tangent to be by taking $x = \cos(3.1415)$, ...
1
vote
1answer
86 views
find distance from point in circle to perimiter
If I have the following circle, with centre in red and a random point in the circle in blue. I know the radius ,r, length of d, and the angle p:
I then create a a new green point and I know the ...
1
vote
2answers
106 views
x Points around a circle
I would like to calculate x number of points around a circle using the circle's radius/diameter.
For example, if I wanted 24 equidistant points around a circle with radius 30, how could I go about ...
2
votes
1answer
414 views
Equation of sine wave around a circle
Consider a sine wave having $4$ cycles wrapped around a circle of radius 1 unit (its center needs not be the origin of a Cartesian coordinate system). Assume that the length of axis of the sine wave ...
9
votes
4answers
266 views
Why do we use the Euclidean metric on $\mathbb{R}^2$?
On the train home, I thought I would try to prove $\pi$ is irrational. I needed a definition, so I used:
$\pi$ is the area of the unit circle.
But what is a circle?
A circle is the set of tuples ...
1
vote
1answer
129 views
dividing an offset circle into triangles
First of all - I am sorry if it is the wrong forum or if this is a very trivial question. I am not a mathematician nor a trigonometry genius - and therefor I would ask a simple answer that someone ...
1
vote
2answers
97 views
coordinates of the point where 2 tangents to a circle cross
I have a circle of radius r.
Given two lines tangent to the circle at points (x1,y1) and (x2,y2),
What are the coordinates of the point where the two tangents cross?
1
vote
1answer
83 views
Length bisection from circular arc
I am not sure if the following result is well known. I stumbled across it from the paper The Perimetric Bisection of Triangles by Dov Avishalom, where the result was stated without proof. I am ...
2
votes
1answer
90 views
calculated reflected point within circle
The problem to solve is this.
Imagine a circle. We know two points on the circumference, anchor A and anchor B, they could be anywhere on the circumference of the circle. Draw a line between these ...
1
vote
2answers
97 views
Calculating circumference from 2d coords
I'm trying to calculate the circumference of a circle given say three reference points from a 2d coordinates that would form an arc.
The problem is the reference points may be slightly inaccurate so ...
0
votes
2answers
477 views
2 concentric circles, inner circle has a tangent, relations between those points
AB is tangent to the inner circle, consider the trigonometric circle.
Knowing the radius of both circles, is there a relation between those 2 point's coordinates ?
Their coordinate being $A = (R ...
0
votes
1answer
102 views
Making a logo with processing, can't figure out a coordinate…
I'm struggling to make a simple logo, I have no deep knowledge of Inkscape so I'm doing it with a little bit of processing.
The problem is I can't figure out how to determine one certain point's ...
1
vote
2answers
166 views
Formula for calculating the center of an arc
Is there a formula for calculating the point equidistant from the start point and end point of an arc given:
1) An arc is defined as: A center point $P$, a radius $r$ from the center, a starting ...
3
votes
3answers
479 views
Finding a point having the radius, chord length and another point
Me and a friend have been trying to find a way to get the position of a second point (B on the picture) having the first point (A), the length of the chord (d) and the radius (r).
It must be possible ...
0
votes
1answer
111 views
Calculating Points in Circles
I am trying to calculate the points around a circle with a certain distance in between each other.
Below is a graphical representation of what I am attempting to do.
The diameter is 70 (radius 35), ...
2
votes
1answer
142 views
Trying to reverse engineer this pattern…
this is my first post on the mathematics node of stack exchange, so please forgive me if I'm not posting an appropriate question, but I'm not sure where else to address this. I'm trying to figure out ...
1
vote
3answers
284 views
Polar equation of a circle
A very long time ago in algebra/trig class we did polar equation of a circle where
$r = 2a\cos\theta + 2b\sin\theta$
Now I forgot how to derive this. So I tried using the standard form of a circle.
...
2
votes
1answer
192 views
Finding points relating to the edge of a circle in an x,y coordinate system
My question is a bit hard for me to express, so please bear with me. I never got far in trig, and haven't done much on the subject in years; trying to get back into it as it's a pretty major part of ...
7
votes
1answer
374 views
How to turn this sum into an integral?
I have been trying to find the closed form of this sum to no avail. It was suggested to me to try and turn this sum into an integral and solve it like that. However, I am confused as to how to do ...
2
votes
1answer
225 views
Convergence and closed form of this infinite series?
If we have a circle of radius $r$ with an $n$-gon inscribed within this circle (i.e. with the same circumradius), we can find the difference of the areas using:
$$A_n =\overbrace{\pi r^2}^\text{Area ...
1
vote
5answers
831 views
Evaluate the $\sin$, $\cos$ and $\tan$ without using calculator?
Evaluate the $\sin$, $\cos$ and $\tan$ without using calculator?
$150$ degree
the right answer are $\frac{1}{2}$, $-\frac{\sqrt{3}}{2}$and $-\frac{1}{\sqrt{3}} $
$-315$ degree
the ...
1
vote
1answer
65 views
Computing angle
See the drawing for the situation. Given lenghts a, b and c and also L, but k and angle alpha are unknown. How to compute this angle alpha?
I know it is possible to compute if we first compute k in ...
1
vote
2answers
203 views
Given an angle, get the trigonometric circle point.
Given an angle, in degrees, how can I get the trigonometric circle point coordinates for it?
For instance, given the angle 0, I would get (1,0). 90 would be (0,-1). Clockwise.
2
votes
1answer
266 views
How do you find the angle of circle segment formed with points (x,y) and (radius,0)?
I've been learning about the unit circle, sine, cosine, and the like in my introduction to trigonometry course, but I'm drawing a blank here.
If I have a circle centered at the origin, with radius r ...
1
vote
2answers
121 views
Trigonometry & circle math
I tried to solve this Trigonometry question, but I do not know how to solve. I read that the
circle has radius 1 and center at (0.0) as the unit circle is plotted in the coordinate
system. I ...
7
votes
4answers
210 views
Does the graph of $\cos x$ intersect the unit circle other than the point (0,1)?
It would seem the unit circle is nicely tucked under the graph of $\cos x$, touching only at (0,1), but is that what's truly going on here?
0
votes
1answer
82 views
Finding a point which is constrained to 3 other points.
Is there an easy way to find the 4th point given 3 fixed points and a different minimum length between the 4th point and each of the 3 points?
Similar to this question, but with non-fixed minimum ...
0
votes
1answer
74 views
Finding a function that computes a point on the unit-circle
I can't find the definition of a function $f(x); x \in [-1;1]$ where $(x|f(x))$ is a point on the unit-circle.
Can you please give me a hint?
---------- Edit -----------
Background:
I want to ...
