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Question: If the period of the function \(f(x) = \sin\left( \frac{x}{n} \right)\) is \(4\pi,\) then n is equal...

If the period of the function f(x)=sin⁡(xn)f(x) = \sin\left( \frac{x}{n} \right) is 4π,4\pi, then n is equal to

A

1

B

4

C

8

D

2

Answer

2

Explanation

Solution

sin⁡(xn)=sin⁡(2π+xn)=sin⁡[1n(2nπ+x)]\sin\left( \frac{x}{n} \right) = \sin\left( 2\pi + \frac{x}{n} \right) = \sin\left\lbrack \frac{1}{n}(2n\pi + x) \right\rbrack

⇒\Rightarrow Period of the function sin⁡(xn)\sin\left( \frac{x}{n} \right)is 2nπ.2n\pi.

⇒\Rightarrow 2nπ=4π⇒n=2.2n\pi = 4\pi \Rightarrow n = 2.