# If tanx=-2/9 sinx>0, how do you find the sin, cos, sec, csc, and cot?

Apr 16, 2015

If $\tan \left(x\right)$ is negative and $\sin \left(x\right)$ is positive,
$x$ must be in Quadrant 2

and evaluation is only a matter of reading the graph.

Assuming $x \epsilon \left[0 , 2 \pi\right]$

$\sin \left(x\right) = \frac{2}{\sqrt{85}}$

#cos(x) = - 9/sqrt(85)

$\csc \left(x\right) = \frac{\sqrt{85}}{2}$

$\sec \left(x\right) = - \frac{\sqrt{85}}{9}$

$\cot \left(x\right) = - \frac{9}{2}$