Trigonometry & Inverse Trigonometry
Inverse Function Properties
Grade 12
Question:
<p>The value of \(\cos\left(\cos^{-1}\left(\frac{1}{8}\right)\right)\) is equal to</p>
<p>(a) \(\frac{1}{8}\)</p>
<p>(b) \(\frac{1}{4}\)</p>
<p>(c) \(\frac{1}{2}\)</p>
<p>(d) 1\)</p>
Step-by-Step Solution
Key Concept: Apply the fundamental property that the cosine function and its inverse cancel each other.
<p>By the definition of inverse cosine, \(\cos(\cos^{-1}(x)) = x\) for all \(x\) in the domain \([-1, 1]\). Therefore, \(\cos\left(\cos^{-1}\left(\frac{1}{8}\right)\right) = \frac{1}{8}\).</p>
Correct Answer: A