Question

The value of \( \cos \left( \cos^{-1} \left( \frac{1}{3} \right) \right) \) is equal to

• A. \( -\frac{3}{4} \)
• B. \( \frac{3}{4} \)
• C. \( \frac{1}{3} \)
• D. \( \frac{1}{4} \)

Hint:

The value of \( \cos(\cos^{-1}(x)) \) is simply \( x \), as long as \( x \) is within the domain of the inverse cosine function.

Answer 1

The Correct Option is C

Step 1: Apply the Inverse Cosine Function.
The inverse cosine function, \( \cos^{-1} \left( \frac{1}{3} \right) \), gives an angle whose cosine is \( \frac{1}{3} \). Taking the cosine of that angle will return \( \frac{1}{3} \).
Step 2: Conclusion.
The correct answer is (C), \( \frac{1}{3} \).