Question

If \( \cos^{-1} x = y \), then _____

• A. \( 0 \le y \le \pi \)
• B. \( 0<y<\pi \)
• C. \( -\frac{\pi}{2} \le y \le \frac{\pi}{2} \)
• D. \( -\frac{\pi}{2}<y<\frac{\pi}{2} \)

Hint:

Remember standard ranges: \(\sin^{-1}x \in [-\frac{\pi}{2}, \frac{\pi}{2}]\), \(\cos^{-1}x \in [0,\pi]\).

Answer 1

The Correct Option is A

Concept: Range of inverse cosine function: \[ \cos^{-1} x \in [0, \pi] \]
Step 1: Apply definition. \[ y = \cos^{-1} x \Rightarrow y \in [0, \pi] \]