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

enter image description here

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?

enter image description here

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    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.2012-06-06

2 Answers 2

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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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    https://commons.wikimedia.org/wiki/File:FatTrifolium.svg2018-12-06