Find the principal value of: sin⁻¹(−1/2)

To find the principal value of sin⁻¹(−1/2), we need to determine the angle whose sine is −1/2. The sine function is negative in the third and fourth quadrants.

Identifying the Angle

The reference angle for sine equal to 1/2 is 30 degrees (or π/6 radians). Since we are looking for the negative value, we consider the angles in the fourth quadrant.

Principal Value

The principal value of sin⁻¹(−1/2) is:

• In degrees: −30 degrees
• In radians: −π/6

Thus, the principal value of sin⁻¹(−1/2) is −π/6 radians or −30°.