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#### skatenerd

##### Active member

- Oct 3, 2012

- 114

$$\hat{i} = \sin{\phi}\cos{\theta}\hat{e_r} + \cos{\phi}\cos{\theta}\hat{e_\phi} - \sin{\theta}\hat{e_\theta}$$

$$\hat{j} = \sin{\phi}\sin{\theta}\hat{e_r} + \cos{\phi}\sin{\theta}\hat{e_\phi} - \cos{\theta}\hat{\theta}$$

$$\hat{k} = \cos{\phi}\hat{e_r} - \sin{\phi}\hat{e_\phi}$$

I'm having a bit of trouble figuring out where to start with this. I totally understand geometrically how to convert \(x\) \(y\) and \(z\) coordinates to spherical, but I feel like that isn't helping me here. How do I begin to find the spherical unit vectors in terms of the cartesian unit vectors, or vise versa?