Question

Range of the function \( \cos^{-1} \):

• A. \( [0, \pi] \)
• B. \( (0, \pi) \)
• C. \( \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \)
• D. \( [0, \pi] \)

Hint:

For inverse trigonometric functions, always remember the standard range: \( \sin^{-1}(x) \) and \( \cos^{-1}(x) \) have ranges \( [-\frac{\pi}{2}, \frac{\pi}{2}] \) and \( [0, \pi] \), respectively.

Answer 1

The Correct Option is A

Step 1: Understanding the function \( \cos^{-1}(x) \).
The inverse cosine function, \( \cos^{-1}(x) \), is defined as the angle \( \theta \) in the interval \( [0, \pi] \) such that \( \cos(\theta) = x \). This range ensures that the function returns a valid angle for all values in the domain \( [-1, 1] \). Step 2: Conclusion.
Thus, the range of \( \cos^{-1}(x) \) is \( [0, \pi] \), corresponding to option (A).