Trigonometry & Inverse Trigonometry
Inverse Trigonometric Functions
Grade 12
Question:
<p>$\cos^{-1}(\cos \theta) = \theta$, for all $\theta$ belonging to</p>
<p>(a) $[0, \pi]$</p>
<p>(b) $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$</p>
<p>(c) $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$</p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: The inverse cosine function has principal branch $[0, \pi]$ and returns the same angle only within this interval.
<p>The principal value branch of $\cos^{-1}$ is $[0, \pi]$. Therefore, $\cos^{-1}(\cos \theta) = \theta$ holds for all $\theta$ in this interval.</p>
Correct Answer: A