How do you calculate arcsin(−1/2)?

Question

Calculate arcsin(−1/2).

Answer choices

1. 5π/6
2. −π/6 + πk
3. π/3
4. π/6
5. −π/6

Answer

arcsin(−1/2) = −π/6 (−30°).

Explanation

The principal value of arcsine lies in [−π/2, π/2]. Since sin(π/6) = 1/2 and sine is odd, sin(−π/6) = −1/2. The angle −π/6 belongs to the required interval, so it is the value of arcsin(−1/2).