How do you find the value of cos^-1(-√3/2)?

To find the value of cos^-1(-√3/2), we need to determine the angle whose cosine is -√3/2.

Understanding the Cosine Function

The cosine function is negative in the second and third quadrants of the unit circle. The reference angle for which cos(θ) = √3/2 is 30 degrees (or π/6 radians).

Finding the Angles

• In the second quadrant, the angle is: 180° - 30° = 150° (or π - π/6 = 5π/6 radians).
• In the third quadrant, the angle is: 180° + 30° = 210° (or π + π/6 = 7π/6 radians).

Determining the Principal Value

The function cos^-1 (or arccos) gives the principal value, which is always in the range of 0 to π (0 to 180 degrees). Therefore, the value we seek is:

cos^-1(-√3/2) = 150° (or 5π/6 radians).