# Tagged Questions

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### Is there any way to express $\theta=c$ as some function of $r$?

I recently found this: Desmos Graphing calculator. I tried to plot the equation $\theta=45$ but it gave me an error: Sorry, you can't graph $\theta$ as a function of anything yet. So I started ...
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### Transforming a polar equation into a Cartesian equation?

Transform the polar equation to a Cartesian (rectangular) equation: $$r= \frac5{5cosθ + 6sinθ}$$ These equations really stump me, so if you could be more "heavy-handed" with the explanation, I'd ...
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Convert the polar equation to rectangular form (rectangular equation) $$r=\frac{9}{1-3\cos(\theta)}$$ I know that $r^2= x^2+y^2, x= r\cos(\theta)$ and $y= r\sin(\theta)$ and $\tan(\theta)= ... 1answer 70 views ### Drawing polar graphs when given theta in terms of the radius I know how to plot when it is like$r=10 \cdot \sin(2\theta)$. But how to do that when the condition is like:$\theta =2 \pi \cdot \sin(r)$? 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 ... 1answer 31 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$1answer 106 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: $$x^2 + y^2 = 1 - 2\sin\theta + \sin^2\theta\quad x = \cos\theta - \sin\theta\cos\theta\quad ... 2answers 327 views ### Find the cartesian equation of: r=2\cos\left(\frac {3\theta}{2}\right) I've managed to use identities to simplify it down to:$$r = 2\left(\cos^3\left({\theta\over2}\right)-3\sin\left({\theta\over2}\right)\cos\left({\theta\over2}\right)\right)$$using trig identities, ... 2answers 5k views ### Cannabis Equation How can an equation for the following curve be derived?$$r=(1+0.9 \cos(8 \theta)) (1+0.1 \cos(24 \theta)) (0.9+0.1 \cos(200 \theta)) (1+\sin(\theta))$$(From WolframAlpha) 2answers 224 views ### Parametrization of a curve in polar coordinates I'm trying to change this parametrics equations to polar coordinates$$ X(t) = 2\cos(t) - \sin(2t) \\ Y(t) = 2\sin(t) - \cos(2t) $$What i tryed to do was raise the two equations squared, sum ... 2answers 1k views ### Convert x^2 - y^2 -2x = 0 to polar? So far I got$$r^2(\cos^2{\phi} - \sin^2{\phi}) -2 r\cos{\phi} = 0r^2 \cos{(2\phi)} -2 r \cos{\phi} = 0$$3answers 2k views ### Writing Polar Equations In Parametric Form For an example problem, in my textbook, the author wanted to demonstrate how to graph a polar function. Deeming it most convenient, my author took the polar function r=2\cos 3\theta, and re-wrote it ... 3answers 73 views ### Put x in terms of u and v I have these two equations$$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 ... 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 ... 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. ... 2answers 4k views ### Difficult conversion from polar equation to rectangular equation. How do we convert this into rectangular equation?$r=5\theta$2answers 196 views ### How do we get the rectangular form of this? I know if$\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)$3answers 2k views ### Writing a Polar Equation for the Graph of an Implicit Cartesian Equation If$(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 ... 3answers 125 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? 2answers 642 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 ...
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 ...
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 ...