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?

2 Answers
Mar 20, 2015

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:
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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( 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#.