Question

The principal value of \( \tan^{-1}(1) \) is:

• A. (0)
• B. (\(\frac{\pi}{6}\))
• C. (\(\frac{\pi}{4}\))
• D. (\(\frac{\pi}{2}\))

Hint:

Memorize the principal value ranges for inverse trigonometric functions:
- \( \sin^{-1}(x) \): \([-\frac{\pi}{2}, \frac{\pi}{2}]\)
- \( \cos^{-1}(x) \): \([0, \pi]\)
- \( \tan^{-1}(x) \): \((-\frac{\pi}{2}, \frac{\pi}{2})\)
These ranges ensure a unique output for each input.

Answer 1

The Correct Option is C