# How do you find the exact values of sintheta and tantheta when costheta=1?

Nov 16, 2016

#### Explanation:

Given $\cos \left(\theta\right) = 1$

To find #sin(theta), use the identity:

${\sin}^{2} \left(\theta\right) + {\cos}^{2} \left(\theta\right) = 1$

${\sin}^{2} \left(\theta\right) + {1}^{2} = 1$

${\sin}^{2} \left(\theta\right) = 0$

$\sin \left(\theta\right) = 0$

To find $\tan \left(\theta\right)$, use the identity:

$\tan \left(\theta\right) = \sin \frac{\theta}{\cos} \left(\theta\right)$

$\tan \left(\theta\right) = \frac{0}{1}$

$\tan \left(\theta\right) = 0$