Trigonometry & Inverse Trigonometry
Composite Inverse Trig Functions
Grade 12
Question:
<p>The value of \(\cos\left(\cos^{-1}\left(\cos\left(\sin^{-1}\left(\frac{63}{8}\right)\right)\right)\right)\) is</p>
<p>(a) \(\frac{3}{16}\)</p>
<p>(b) \(\frac{3}{8}\)</p>
<p>(c) \(\frac{3}{4}\)</p>
<p>(d) \(\frac{3}{2}\)</p>
Step-by-Step Solution
Key Concept: Compose inverse trigonometric functions carefully, checking domain restrictions at each step.
<p>Note that \(\sin^{-1}\left(\frac{63}{8}\right)\) is undefined since \(\frac{63}{8} > 1\) is outside the domain of inverse sine. The problem statement appears to contain an error in the original text. Assuming it should be a valid composition, apply inverse function properties step by step.</p>
Correct Answer: B