0
votes
1answer
26 views

Find points near end point of a line

Any equation to find points near to both start and end points of lines with different slopes. See image. Need P and Q. If Endpoints are named A and B, AP and BQ should be 1 cm
1
vote
4answers
33 views

Find minimum x value from a polar function

I am mainly examining limacon functions. For the equation r= b + a*cos(theta), it is easy to find the minimum radius, but I want to find the most negative value (between a given range). Take function ...
2
votes
1answer
34 views

Representation of cardiod in the complex plane

I noticed that the complex function $$f(z) = \frac{2}{(z+i)^2}$$ seems to map the real line onto the cardioid given by the polar equation: $$r = 1- \cos(\theta).$$ I was wondering if there is a simple ...
2
votes
1answer
56 views

Polar to cartesian form of $ r = \sin(2\theta)$

As title describes, I was wondering how I would put this into cartesian form, from polar. All I have is $ r = \sin(2\theta)$. I'm not really sure what to do, i've been trying to find similar ...
-1
votes
1answer
52 views

I need help converting $x^2 + y^2 = -4y$ into a polar equation

I know the whole $r^2 = x^2 + y^2$ and $x = r \cos \theta$ and $y = r \sin \theta$, but I just can't seem to apply those rules to the equation $x^2 + y^2 = -4y$ to make it a polar one.
0
votes
1answer
33 views

Relationship between two perpendicular lines expressed in polar coordinate?

I've been studying Hough transform. Basically, let's say we have a line $$y = mx+b$$ We can change our view to a parametric view (e.g. parameter space of $m,b$ while $(x,y)$ is constant). This would ...
0
votes
1answer
39 views

Polar graph question

Can you only graph periodic functions using polar graphing? I'm not really understanding this I guess. It you are to get all of the x and y values on a finite graph, then the original must be ...
0
votes
1answer
47 views

Trigonometry for steradian angle

Polar coordinate system is very closely associated with trigonometry. For instance, given an angle in radian, we can find its corresponding 2-D cartesian coordinates using ...
2
votes
4answers
173 views

Linear combinations of sine and cosine

If you take a linear combination of the cosine and sine function, then the result is again a sinusoid, but with a new amplitude and phase shift. $$a \cos(\theta) + b \sin(\theta) = A \cos(\theta + ...
1
vote
3answers
120 views

How to calculate $\theta$ when we know $\tan \theta$.

Hej I'm having difficulties calculating the angle given the tangent. Example: In a homework assignement I'm to express a complex variable $z = \sqrt{3} -i$ in polar form. I know how to solve this ...
0
votes
2answers
273 views

Find the cartesian equation of: $r=2\cos\left(\frac {3\theta}{2}\right)$

I've managed to use identities to simplify it down to: $$r = 2\left(\cos^3\left({\theta\over2}\right)-3\sin\left({\theta\over2}\right)\cos\left({\theta\over2}\right)\right)$$ using trig identities, ...
1
vote
1answer
86 views

How can I derive differential equations for polar coordinates based on these equations?

A textbook I am using on my own to study differential equations contains a problem: given the two differential equations for $x,y$ below and a real value of $t$, derive the differential equations for ...
1
vote
1answer
66 views

translate coordinates on circle to percentage?

I'm coming more from a programming point of view but the question is pure math. The only strange thing, I guess, is that the coordinate system is like this: ...
1
vote
1answer
81 views

Write function from polar to rectangular coordinates.

I need to write this functions in rectangular coordinates: $$f(r,\theta)=r^{2k+5}\cos5\theta$$ $$g(r,\theta)=r^{2k+5}\cos5\theta$$ Of course the radius is very easy to convert to $x$ and $y$. The ...
1
vote
1answer
290 views

Area of a square in polar coordinates?

I was attempting, for the exercise of it, to find the area of the a simple square with an infinite number of infinitesimal circle sectors. Let us say this square is $[5 x 5]$. Alas, it's been ...
0
votes
0answers
18 views

Getting latitude/longitude from a 2d co-ord system [duplicate]

Given a latitude/longitude and a distance and bearing in relation to that point, how can I find the latitude/longitude of the new position? Distances can range from 0-100km so curvature of the earth ...
4
votes
1answer
69 views

Polar coordinations - problem with r and $\theta$

let's take a look on Archimedean spiral. the polar equation is $r = \theta$. click here to look. but $\tan (\theta) = y/x$ and $r = \sqrt{x^2+y^2}$, so $r = \theta \rightarrow \tan(\sqrt{x^2+y^2}) ...
0
votes
2answers
24 views

Polar coordinates that uses $\frac { 1 }{ Z_1 }$

I am doing polar coordinates, and I am stuck when my book asks to do $\frac { 1 }{ Z_1 }$. I have no problems with $\frac { Z_1 }{ Z_2 }$ and $Z_1Z_2$. Here is the values for $Z_1$ I'm not so much ...
3
votes
2answers
11k views

Ellipse in polar coordinates

I think Wikipedia's polar coordinate elliptical equation isn't correct. Here is my explanation: Imagine constants $a$ and $b$ in this format - Where $2a$ is the total height of the ellipse and $2b$ ...
1
vote
3answers
130 views

Converting $x^2 + 6y - 9 = 0$ to polar.

So far I got here \begin{align} (r\cos\phi)^2 & + 6 r \sin\phi- 9 = 0\\ (r\cos\phi)^2 & = 9 - 6r \sin\phi \end{align}
2
votes
1answer
127 views

Converting polar to cartesian?

So far I got \begin{align} r & = 7 / (4 - 2 \cos\theta) \\ r (4 & - 2\cos\theta) = 7 \\ r (4 & - 2( x / r ) ) = 7 \end{align} I apologize in advance for the bad formatting.
2
votes
2answers
1k views

Convert $ x^2 - y^2 -2x = 0$ to polar?

So far I got $$r^2(\cos^2{\phi} - \sin^2{\phi}) -2 r\cos{\phi} = 0$$ $$r^2 \cos{(2\phi)} -2 r \cos{\phi} = 0$$
0
votes
1answer
190 views

Collision detection of two circular sectors in mixed polar and Cartesian coordinate

I am trying to solve the following collision detection problem. Suppose we have two circular sectors, each described in their own polar coordinate system with four values $r_1$, $r_2$, $d_1$ and ...
1
vote
1answer
1k views

General Cartesian/Rectangular Equation for Polar Rose ($r=\sin(k\theta)$)

How do I convert the Polar Equation $r=\sin(k \theta)$ to Cartesian Equation? I understand that $r^2=x^2+y^2$ and that $x=r\cos\theta$ and $y=r\sin\theta$, but no matter how I try to arrange them it ...
1
vote
4answers
5k views

Find the area of the region inside the limaçon

I'm struggling to figure out the answer to this: Find the area of the region inside the limaçon, $r=3 + \sin(\theta)$ Could someone please help me out?
4
votes
2answers
767 views

Find the area enclosed by the loop $r=2(1-\sin\theta)\sqrt{\cos\theta}$

The diagram shows a sketch of the loop whose polar equation is $$r=2(1-\sin\theta),\qquad -\frac{\pi}{2}\leq\theta\leq\frac{\pi}{2}$$ a)Show that the area enclosed by the loop is 16/3. ...
1
vote
3answers
1k 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. ...
0
votes
2answers
60 views

Find the Cartestian form of $6 - 7i$ rotated anticlockwise through $\frac{3\pi}{4}$ about the origin

Find the cartestian form of $6 - 7i$ rotated anticlockwise through $\frac{3\pi}{4}$ about the origin I realize that I am going to be doing something like: $\sqrt{85}e^{i\alpha}.e^{i\frac{3\pi}{4}}$ ...
1
vote
1answer
124 views

Given an exact velocity and a “velocity range”, what is the relative velocity range?

I'm trying to calculate the relative velocity ($V_R$) between an exact velocity ($V_0$) and a velocity range ($V_1$). The exact velocity ($V_0$) is represented simply by ($course$, $speed$). The ...
3
votes
3answers
2k views

Writing a Polar Equation for the Graph of an Implicit Cartesian Equation

If $(x^2+y^2)^3=4x^2y^2,$ then $r=\sin 2\theta$ for some $\theta$. Using $r^2=x^2+y^2, x=r\cos\theta,y=r\sin\theta$, it's easy to get $r^2=\sin^22\theta$. But I don't know what to do next, since ...
2
votes
1answer
2k views

Horizontal and vertical asymptotes of polar curve $r = \theta/(\pi - \theta) \, , \, \in[0,\pi]$

I as supposed to find the vertical and horizontal asymptotes to the polar curve $$ r = \frac{\theta}{\pi - \theta} \quad \theta \in [0,\pi]$$ The usual method here is to multiply by $\cos$ and ...
0
votes
0answers
111 views

Set of all points which are a specified angle away from a given point on a sphere.

I have a sphere with a known point on the surface in polar coordinates. I'm looking to find the set of all points which are exactly some angle away from this point in polar form (this should describe ...
1
vote
2answers
785 views

Express this curve in the rectangular form

Express the curve $r = 9/(4+\sin \theta)$ in rectangular form. And what is the rectangular form? if I get the expression in rectangular form, how am I able to convert it back to polar ...
4
votes
1answer
323 views

Get polar equation from cartesian equation

I have this equation: $x^4 + y^4 = x^2 + y^2$ and I need to convert it to a polar one... I have tried and the result is $$r = \sqrt{\frac{1}{\cos^4\theta + \sin^4\theta}}$$ Is this ok?