Tagged Questions
3
votes
0answers
53 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
75 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
269 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
52 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
652 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
280 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
2k views
Difficult conversion from polar equation to rectangular equation.
How do we convert this into rectangular equation?
$r=5\theta$
0
votes
2answers
124 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
1k 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
85 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
389 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
842 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
100 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 ...
