# Tagged Questions

Questions on polar coordinates, a coordinate system where points are represented by their distance from the origin ($r$) and the angle the line joining the point and the origin makes with the positive horizontal axis ($\theta$).

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### trying to figure out how to set up polar area given two equations

$R=3$ and $R=4-2sin(\theta)$ Find the area I got the second part of the equation right ($1/2$ the integration of $\pi/6$ to $5\pi/6$ of $(4-2sin(x))^2)$ but he first part confuses me. The answer ...
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### Azimuth angle limit in Spherical co-ordinate system

In spherical co-ordinate system $(r, \theta, \phi)$, $\theta$ can range from $0$ to $2\pi$, but $\phi$ only varies from $0$ to $\pi$. Why is that?
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### Triple integral using Cylindrical Coordinates

Evaluate the iterated integral $x= 0$ to $x=1$, $y= -\sqrt{1-x^2}$ to $y=\sqrt{1-x^2}$ and $z= 0$ to $z=2-x^2-y^2$ and $f(x,y,z)= \sqrt{x^2+y^2}$ What I know: I know that I have to use cylindrical ...
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### Polar Coordinates Volume of Solid, Angle for integration?

I'm trying to understand how to find the angle for the integration in polar coordinate form for a solid. Here's an example of what I'm trying to solve: Find the volume of the solid bounded by the ...
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### Cartesian and Polar Coordinates, proving the same number-pair

The question states: Prove that a necessary and sufficient condition for a point to be represented by the same number-pair (a,b) both cartesian and polar coordinates is that it lies on the initial ...
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### Solve $z^5=-32$ and draw its solutions in complex space, then describe their characteristic geometrical property.

I'm solving past exam questions in preparation for an Applied Mathematics course. I came to the following exercise, which poses some difficulty. If it's any indication of difficulty, the exercise is ...
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### Can we convert polar to rectangular when we are given $(1,\theta )$ where $r=1$ and $0\le \theta <2\pi$?

Can we convert polar to rectangular when we are given $(1,\theta )$ where $r=1$ and $0\le \theta <2\pi$?
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### How to think in terms of Polar Coordinates?

I am currently studying Polar Coordinates and many times I've noticed that one converts polar equations in cartesian form to do further analysis. Is there a way to think in terms of Polar Coordinates? ...
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### For which $\alpha \in \mathbb{R}$ does $\int_{\mathbb{R}^n} \big(1+|x|\big)^{\!-\alpha} \mathrm{d}x$ exist?

I assume only $\alpha \gt 1$ gives $\int_{\mathbb{R}^n} (1+|x|)^{-\alpha} \mathrm{d}x \lt \infty$ (simply because this is true for $n=1$). I also assume some clever transformation could be used for ...
How to find out polar angle of a given point $A(x_1,y_1)$ relative to another point $B(x_2,y_2)$ in a 2D space?