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

Feb 21, 2018

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

Explanation:

Since $\tan \theta = \frac{\sin \theta}{\cos \theta}$,

$\tan \theta = 0 \implies \sin \theta = 0$

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 $\pi$, $3 \pi$ etc)) $\cos \theta$ will be -1, otherwise it will be +1.