# If sinB=3/4 and the terminal side of the angle is in quadrant II, how do you find the other five trigonometric functions of B?

Oct 7, 2015

$\textcolor{w h i t e}{\text{XXXXXXXXXXXXXXXXXXXX}} \sec \left(B\right) \frac{4}{3}$
$\cos \left(B\right) = - \frac{\sqrt{7}}{4} \textcolor{w h i t e}{\text{XXXXXXXXXX}} \sec \left(B\right) = \frac{4}{\sqrt{7}} = \frac{4 \sqrt{7}}{7}$
$\tan \left(B\right) = - \frac{3}{\sqrt{7}} = - \frac{3 \sqrt{7}}{7} \textcolor{w h i t e}{\text{XXXX}} \cot \left(B\right) = - \frac{\sqrt{7}}{3}$

#### Explanation:

Setting the hypotenuse to $4$ units
If $\sin \left(B\right) = \frac{3}{4}$ and $B$ is in Q II
the opposite side ($y$) is $3$
and
the adjacent side ($x$) is $- \sqrt{7}$ (by Pythagorean Theorem)

All trigonometric functions of $B$ follow directly from this.