# Find the exact value of: csc^2(17pi/4) How do I do problems with the sin, cos, tan...etc raised to the power of 2?

Mar 20, 2015

I would try to simplify your angle.
$\frac{17}{4} \pi$ is big so I can reduce it (see point 1 and 2 in the diagram below)) to the equivalent $\frac{\pi}{4}$ (certainly fiendlier than the other!) and get:

Mar 20, 2015

Keep in mind that when we write a trig function to a (positive) power, we mean evaluate the trig function, then raise the value to the power.

${\sin}^{2} \left(\frac{\pi}{6}\right) = {\left(\sin \left(\frac{\pi}{6}\right)\right)}^{2} = {\left(\frac{1}{2}\right)}^{2} = \frac{1}{4}$

So, to find ${\csc}^{2} \left(\frac{17 \pi}{4}\right)$ Find ${\left(\csc \left(\frac{17 \pi}{4}\right)\right)}^{2}$ .

That is: find $\csc \left(\frac{17 \pi}{4}\right)$ . and then square that number.

Note:
This convention does not include $t r i {g}^{-} 1$.

We use the $- 1$ in the upper right to indicate the inverse function (the opposite function).
Example:
$\sin \left(\frac{\pi}{6}\right) = \frac{1}{2}$.

So, ${\sin}^{-} 1 \left(\frac{1}{2}\right) = \frac{\pi}{6}$.