# Tag Info

## Hot answers tagged polar-coordinates

Accepted

### Area of loop in graph

First determine where the curve self-intersects. Remember that in polar coordinates, $r$ is an indication of distance from the origin. From the plot, it's evident that the origin is where the self-...
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### Area of loop in graph

Another way of calculation. Changing to cartesian coordinates we have $x^3+y^3=3xy$ which gives a nodal cubic symmetric respect to the diagonal $y=x$. In order of calculate easier the integral we ...
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### The length of the curve

Let $t:=\operatorname{arsinh}(r/\sqrt2)$ ($0\le t\le\operatorname{arsinh}\sqrt2$). Then, $$r=\sqrt2\sinh t,\quad r'_t=\sqrt2\cosh t,$$$$\theta=\sinh t\cosh t+t+\ln\sqrt2,\quad\theta'_t=2\cosh^2t,$$ ...
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### Epsilon-Delta proof for Multivariate Limit in Polar Coordinates

Your argument is wrong, because you made an $|r|$ appear out of thin air. Without it, your expression does not go to zero. Using polar coordinates here is overkill. What you should note is that the ...
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### Need hint: Prove that $r = a (\sin t) + b (\cos t)$ is a circle, where $ab \neq 0$

It's been 11 years, I think it's safe to say it doesn't matter anymore if the entire solution is given. I've managed to get through the problem, so if it can help anyone looking for a fuller ...
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### Show that $y=\frac{1}{x}$ is a hyperbola

The hyperbola $xy=1$ is rotated at an angle of $45^∘=\pi/4$ relative to the $x$-axis. We can use a transformation to rotate our coordinate system by $45^∘$ to find the equation of this hyperbola ...
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### Solve Double Integral with Polar System

The area is bounded by a circle around $(1/2,1/2)$ with radius $1/\sqrt{2}\,:$ $$0=x^2-x+y^2-y=(x-\tfrac12)^2+(y-\tfrac12)^2-\tfrac12\,.$$ Expressing the integral in $(r,\theta)$ has to take into ...
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### Error in graphing the polar equation $r=-1+\cos(\theta)$. I get a different answer than the book for cos(30degrees). Am I wrong?

It's wrong. Here is why. You can directly put the value and check. It's wrong for $90°$ part as well. For a more general approach:- $f(x)=-1+\cosθ$ has maximum value of $0$ at $θ=0°$ and minimum ...
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### Solving Laplace's equation on semi-annular domain

The solution form you have written is for a disk not an annulus or half-annulus Separation of variables can be used in your half-annulus too, and the form you will get is A + B\ln r + \sum_{n=1}^{\...
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1 vote
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### Can I see an example of transforming a tensor from polar to cartesian coordinates?

Is seems like you are familiar with the transformations of basis one forms $dr,d\theta$ to $dx,dy\,.$ The similar formulas for the basis vector fields $\partial_r,\partial_\theta,\partial_x,\partial_y$...
• 15.3k

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