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Relations and Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsRelations and Functions1 Mark
MCQ
The function $ \text{f}(\text{x}) = \sin \Big(\frac{\pi‎\text{x}}{2}\Big) +\cos \Big(\frac{\pi‎\text{x}}{2}\Big)$ is periodic with period:
  • ✓
    $4$
  • B
    $6$
  • C
    $12$
  • D
    $24$
✓

Answer

Correct option: A.
$4$
Period of $\sin \Big(\frac{\pi‎\text{x}}{2}\Big) = 2\pi\Big(\frac{\pi}{2}\Big) = 4$
Period of $\cos \Big(\frac{\pi‎\text{x}}{2}\Big) = 2\pi\Big(\frac{\pi}{2}\Big) = 4$
So, period of $f(x) = \text{LCM} (4, 4) = 4$

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