Question

How do you find the exact values of `costheta` and `sintheta` when `tantheta=0`?

Answer 1

`sin theta =0`, `cos theta = pm 1` - that's all that can be said from `tan theta = 0` in the absence of any other information.

Explanation:

Since `tan theta = {sin theta}/{cos theta}`,

`tan theta = 0 implies sin theta =0`

Thus

`cos^2 theta = 1-sin^2 theta =1`

And so `cos theta = pm`

Actually `tan theta =0` tells you that `theta` is a multiple of `pi`. If it is an odd multiple, (like `pi`, `3pi` etc)) `cos theta` will be -1, otherwise it will be +1.