Question

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?

Answer 1

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

Answer 2

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( pi/6)=(sin (pi/6))^2=(1/2)^2=1/4`

So, to find `csc^2((17 pi)/4)` Find `(csc((17 pi)/4))^2` .

That is: find `csc((17 pi)/4)` . and then square that number.

Note:
This convention does not include `trig^-1`.

We use the `-1` in the upper right to indicate the inverse function (the opposite function).
Example:
`sin( pi/6)=1/2`.

So, `sin^-1(1/2) = pi/6`.