0
votes
1answer
19 views

How to calculate Polar coordinates for Complex Polynomials of Higher Degree?

When such I have a complex number such as $3 - 4i$, I can calculate the $r$ with $r=\sqrt{X^2+Y^2} = \sqrt{3^2+4^2}$. But how do I solve this when I have a complex number such as $(2+6i)^6$
1
vote
1answer
39 views

Find rectangular equation of a cardioid

Given the equation in polar form $$r = 1 - \sin\theta,$$ find the rectangular equation. So far, I found: $$x^2 + y^2 = 1 - 2\sin\theta + \sin^2\theta\quad x = \cos\theta - \sin\theta\cos\theta\quad ...
0
votes
2answers
103 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, ...
25
votes
2answers
5k views

Cannabis Equation

How can an equation for the following curve be derived? $$r=(1+0.9 \cos(8 \theta)) (1+0.1 \cos(24 \theta)) (0.9+0.1 \cos(200 \theta)) (1+\sin(\theta))$$ (From WolframAlpha)
4
votes
2answers
200 views

Parametrization of a curve in polar coordinates

I'm trying to change this parametrics equations to polar coordinates $$ X(t) = 2\cos(t) - \sin(2t) \\ Y(t) = 2\sin(t) - \cos(2t) $$ What i tryed to do was raise the two equations squared, sum ...
2
votes
2answers
779 views

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

So far I got $$r^2(\cos^2{\phi} - \sin^2{\phi}) -2 r\cos{\phi} = 0$$ $$r^2 \cos{(2\phi)} -2 r \cos{\phi} = 0$$
4
votes
3answers
1k views

Writing Polar Equations In Parametric Form

For an example problem, in my textbook, the author wanted to demonstrate how to graph a polar function. Deeming it most convenient, my author took the polar function $r=2\cos 3\theta$, and re-wrote it ...
0
votes
3answers
72 views

Put x in terms of u and v

I have these two equations $$u = \frac{2x}{x^2 + y^2} \\ v = \frac{-2y}{x^2 + y^2}$$ And I need to put $x$ in terms of $u$ and $v$. If I take polar co-ordinates and plug them in I get(in the case of ...
5
votes
2answers
1k views

Is $r=2\cos(\theta)$ a one-petal polar function?

I'm currently learning about polar functions and their graphs in precalculus, and one of the questions on my homework is to identify the shape of the function $r=2\cos(\theta)$. We were taught that ...
1
vote
3answers
643 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. ...
1
vote
2answers
3k views

Difficult conversion from polar equation to rectangular equation.

How do we convert this into rectangular equation? $r=5\theta$
0
votes
2answers
178 views

How do we get the rectangular form of this?

I know if $\sqrt{x^2+y^2} = x$, then the polar equation of this is $r=cos\theta$ So,how to get the rectangular form of this polar equation, is it complicate: $r=cos(10\theta)$
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 ...
1
vote
3answers
114 views

Converting a polar coord to the range $0\le\theta\le2\pi?$

I know that you can keep adding/subtracting numbers to a polar coord, but what if I want to be able to take a number and just convert it to its positive equivalent?
2
votes
2answers
522 views

Did I sketch this polar curve correctly?

The equation is: $r^2=-4 \sin(2\theta)$ I first made a reference graph in cartesian coordinates using values $\displaystyle \frac{\pi}{4}$, $\displaystyle \frac{\pi}{2}$, $\displaystyle \frac{3 ...
1
vote
2answers
1k views

Converting polar equation to cartesian coordinate polar equation and back again?

OK, so I have the following polar equation: $r = Θ/20$ And I would like to translate this a little to the right, and down from the polar origin. Now, I figure since I know cartesian coordinate ...
1
vote
2answers
113 views

What is a good way to pick points for polar equations?

If I want to plot $r = 4\sin3\theta$ what is a good way to pick points? The period is $2\pi/3$ so it will repeat after that, but how do I pick points so that I get a good range of values so that I ...