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## Homework Statement

By using chain rule of differentiation, show that:

$$ \frac{\mathrm{d} sin\phi }{\mathrm{d} t} = \dot{\phi} cos\phi , \frac{\mathrm{d} cos\phi }{\mathrm{d} t} = -\dot{\phi} sin\phi , $$

## Homework Equations

## The Attempt at a Solution

I got this right for a homework problem, but I'm still confused about why the ##\dot{\phi}## comes out. Does the ##\phi## come out because we are doing:

$$ \frac{\mathrm{d} sin \phi }{\mathrm{d} \phi} \frac{\mathrm{d} \phi }{\mathrm{d} t} $$

Also, when do you know if you're working with cartesian unit vectors or ##r## and ##\phi## unit vectors..?

They have nothing to do with time derivatives right?