# 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 ($\theta$).

37 views

### Area inside polar curve

Find the area of the region inside $r=7\sin\theta$ but outside $r=1$. I have tried finding the area of both using $A=\frac{1}{2}\int_\alpha^\beta r^2 dr$, tried arc length...but i cant seem to find ...
22 views

### Polar Equations (Complex)

So I'm trying to figure out what the angle $θ$ would equal at $x=-2$ for the polar equation $r=θ+sin(2θ)$. All I know is that $θ$ has a domain of $0\leθ\le \pi$ and $y < 1$ (pretty sure). I ...
15 views

### Find the Area Bounded by a Polar Curve Over a Given Interval [on hold]

Find the area of the region bounded by the given curve: $r=7e^{\theta}$ on the interval $6\pi/7 \leq θ \leq 2\pi$
22 views

15 views

### Angle vector in polar system represented by Cartesian vector

$x=r\cos\theta,\,y=r\sin\theta\implies r^2=x^2+y^2,\,\theta=\arctan(y/x)$ I can show that $\hat{r}=\cos\theta\hat i+\sin\theta\hat j$, where the hat vectors are ...
13 views

24 views

### What is the polar coordinate equation for an Archimedean spiral with arc length known relative to theta?

What is the equation for the radius of a polar coordinate for an Archimedean spiral with the arc length known relative to theta? arc length: L = ...
52 views

### Prove a function is harmonic

This problem is from Conformal Mapping by Zeev Nehari: If $u(x,y)$ is harmonic and $r=(x^2+y^2)^{1/2}$, prove $u(xr^{-2}, yr^{-2})$ is harmonic. The hint is obvious: "Use polar coordinates." I ...
65 views

30 views

### Polar equation for a k-leaf rose: is it possible to define an inner radius?

Is it possible to define a polar equation for a k-leaf rose with an inner radius for a k-leaf rose (as in this image)? I'm familiar with the general equation for a k-leaf rose $$r = \cos(k*\theta)$$ ...