Evaluate arcsin(cos(-pi/2))

$\arcsin (\cos (- \frac{π}{2}))$

Step 1

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\arcsin (\cos (\frac{3 π}{2}))$

Step 2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\arcsin (\cos (\frac{π}{2}))$

Step 3

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$\arcsin (0)$

Step 4

The exact value of $\arcsin (0)$ is $0$ .

$0$