Question

If \(f(x) = \cos[\pi^2]x + \cos[-\pi^2]x\), then

• A. \(f(\pi/4) = 2\)
• B. \(f(-\pi) = 2\)
• C. \(f(\pi) = 1\)
• D. \(f(\pi/2) = -1\)

Hint:

\([\cdot]\) denotes greatest integer function.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
\(\pi^2 \approx 9.8696\), so \([\pi^2] = 9\), \([-\pi^2] = -10\).
Step 2: Detailed Explanation:
\(f(x) = \cos(9x) + \cos(-10x) = \cos(9x) + \cos(10x)\)
\(f(\pi/2) = \cos(9\pi/2) + \cos(5\pi) = \cos(\pi/2 + 4\pi) + \cos(5\pi)\)
= \(0 + (-1) = -1\)
Step 3: Final Answer:
\(f(\pi/2) = -1\).