# How to “rotate” a polar equation?

Take a simple polar equation like r = θ/2 that graphs out to:

But, how would I achieve a rotation of the light-grey plot in this image (roughly 135 degrees)? Is there a way to easily shift the plot?

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$r=(\theta-\frac{3\pi}{4})/2$ – Arturo Magidin Jun 6 '12 at 16:35
Rotation about the origin is simple in polar coordinates, just like translation to the right (or up, or both) is simple in the usual rectangular coordinates. – André Nicolas Jun 6 '12 at 16:42

## 1 Answer

Just put $\theta-135^\circ$ in place of $\theta$. Or if you're working in radians, then the equivalent in radians.

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Ah, I don't know why I didn't think to try that. And thanks for the helpful note about radians, I was (apparently) working in radians and would have been stumped by trying degrees. – Nick Jun 6 '12 at 23:26