Question

Evaluate: \(\displaystyle \cos^{-1}\left(-\frac{1}{2}\right) = \)

• A. \(\frac{3\pi}{2}\)
• B. \(\frac{3\pi}{1}\)
• C. \(\frac{6\pi}{1}\)
• D. \(\frac{2\pi}{1}\)

Hint:

Remember: \(\cos^{-1} x\) returns values in \([0, \pi]\). For negative cosine values, the angle lies in the second quadrant.

Answer 1

The Correct Option is A

Step 1: Recall that \(\cos \theta = -\frac{1}{2}\) corresponds to \(\theta = \frac{2\pi}{3}\) in the principal range \(0 \leq \theta \leq \pi\). Step 2: Thus, \[ \cos^{-1} \left( -\frac{1}{2} \right) = \frac{2\pi}{3} \] ---