Inverse Trigonometric Functions
Domain and Range Limits
Premium Question
Grade 12
Question:
If $\cos^{-1} p + \cos^{-1} q + \cos^{-1} r = 3\pi$, then $p + q + r$ equals:
(1) $3$
(2) $-3$
(3) $0$
(4) $1$
Step-by-Step Solution
Key Concept: The range of $\cos^{-1}$ is $[0, \pi]$. For the sum to reach $3\pi$, each term must be at its maximum. What input gives $\cos^{-1}(t) = \pi$?
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)