# If cos theta = 5/13, theta in quadrant II, how do you find sin theta and tan theta?

Jun 13, 2016

$\cos \theta < 0$ in Q2, so there is no answer, but read on...

#### Explanation:

If $\theta$ were in Q1 then we would simply be dealing with the internal angles of a $5$, $12$, $13$ right angled triangle.

Note that:

${5}^{2} + {12}^{2} = 25 + 144 = 169 = {13}^{2}$

Hence in Q1 we would have:

$\sin \theta = \frac{12}{13}$ and $\tan \theta = \frac{12}{5}$

In Q2, $\cos \theta < 0$, so cannot be equal to $\frac{5}{13}$, so there is an error in the question.

In Q4, we would find $\sin \theta = - \frac{12}{13}$ and $\tan \theta = - \frac{12}{5}$.