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Relations and Functions — MATHS STD 11 Science — Question

Rajasthan 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:
  • A
    4
  • B
    6
  • C
    12
  • D
    24
✓

Answer

  1. 4

Solution:

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) = LCM (4, 4) = 4

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