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JEE Main & Advanced Mathematics Trigonometric Equations Question Bank Periodic functions

  • question_answer
    If the period of the function \[f(x)=\sin \left( \frac{x}{n} \right)\]is \[4\pi \], then n is equal to [Pb. CET 2000]

    A) 1

    B) 4

    C) 8

    D) 2

    Correct Answer: D

    Solution :

    \[\sin \,\left( \frac{x}{n} \right)=\sin \,\left( 2\pi +\frac{x}{n} \right)\] = \[\sin \left( \frac{1}{n}(2n\pi +x) \right)\] Þ  Period of the function sin \[\left( \frac{x}{n} \right)\]is \[2n\pi \]. Þ  \[2n\pi =4\pi \]\[\Rightarrow n=2\].


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