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[tex]\hat{\theta} = -sin(\theta)\hat{x} + cos(\theta) \hat{y} [/tex]

[tex]\hat{r} = cos(\theta) \hat{x} + sin(\theta) \hat{y} [/tex]

... and I think I can do that for spherical coordinates too. But I can't see how to do it the other way around (polar to cartesian). If you could just help me do it for polar coords I think I will be able to adapt it to spherical.

Thanks!