Find arcsin [cos (Pi/2)]

Question

The answer is 0.

How do you solve this problem? Thanks.

Answer 1

You have to use the definition of cos and sin. If you use the geometric definition using a right triangle, then you see that

cos(x) = sin(pi/2-x)

If you take the cosine of one angle (alpha), you get the same as when you take the sin of the other angle (beta). Now, alpha is 90° - beta, so the result follows.

So, arcsin[cos(pi/2)] =
arcsin[sin(0)] = 0

Answer 2

You are standing 35 feet from a billboard. The angle of elevation is 58 degrees. How tall is the billboard? Round your answer to the nearest foot