Tagged Questions
4
votes
1answer
32 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
19 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 ...
1
vote
1answer
1k 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 $2b$ ...
0
votes
0answers
73 views
How to remember symmetry tests for polar graphs?
Polar $(r , -\theta)$ & $(-r, \pi - \theta)$
Pole $(-r, \theta)$ & $(r, \pi + \theta)$
$\frac{\pi}{2} (-r, \theta)$ & $(r, \pi - \theta)$
1
vote
3answers
111 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
51 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
77 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
79 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
320 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 ...
0
votes
0answers
149 views
Convert cartesian coordinate to geography coordinate
i have a Canvas on my web where i get the position of the pixel when i draw. Example, X=1, Y=5. So, i have to project that on a real wall. I know the geography coordinate of each lower corner of the ...
1
vote
4answers
1k 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
475 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
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.
...
0
votes
2answers
33 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
87 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
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 ...
2
votes
1answer
837 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
66 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
393 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
253 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?
