Question:
Evaluate: \(\displaystyle \cos^{-1}\left(-\frac{1}{2}\right) = \)
Evaluate: \(\displaystyle \cos^{-1}\left(-\frac{1}{2}\right) = \)
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Remember: \(\cos^{-1} x\) returns values in \([0, \pi]\). For negative cosine values, the angle lies in the second quadrant.
Updated On: Nov 9, 2025
- \(\frac{3\pi}{2}\)
- \(\frac{3\pi}{1}\)
- \(\frac{6\pi}{1}\)
- \(\frac{2\pi}{1}\)
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The Correct Option is A
Solution and Explanation
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,
\[
\cos^{-1} \left( -\frac{1}{2} \right) = \frac{2\pi}{3}
\]
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