Q230 / 270 · NDA 2023 (Phase 1) · Mathematics
Paragraph:
Let $f(x)=\sin \left[\pi^2\right] x+\cos \left[-\pi^2\right] x$ where [.] is a greatest integer function.
Question:
What is $f\left(\frac{\pi}{4}\right)$ equal to?
Question: What is $f\left(\frac{\pi}{4}\right)$ equal to?
- A$-\frac{1}{\sqrt{2}}$
- B$-1$
- C$1$
- Correct answerD$\frac{1}{\sqrt{2}}$
Solution
$f\left(\frac{\pi}{4}\right)=\sin \frac{9 \pi}{4}+\cos \frac{10 \pi}{4}$
$=\sin \left(2 \pi+\frac{\pi}{4}\right)+\cos \left(2 \pi+\frac{\pi}{2}\right)$
$=\sin \frac{\pi}{4}+\cos \frac{\pi}{2}=\frac{1}{\sqrt{2}}$
Hence, the correct answer is option: 'D'.