Question

: The period of $sinkx$ is
A. $\dfrac{\pi }{k}$
B. $\dfrac{{2\pi }}{k}$
C. $\dfrac{{2\pi }}{{\left| k \right|}}$
D. $\dfrac{\pi }{{\left| k \right|}}$

Answer 1

Hint : To answer the period of $sinkx$ first of all we should know the period of $sinx$. Once we noted the period of $sinx$ just divide that period by the coefficient multiplied with x in $sinx$. That will be the period of given sin function.

Complete step-by-step answer :
Given function is $sinkx$.
We have to calculate the period of $sinkx$.
We know that the period of $sinax$ is $\dfrac{{2\pi }}{{\left| a \right|}}$ means the coefficient multiplied with x should be in division.
So now to calculate the period of $sinkx$ we have to know the period of $sinx$first.
The period of $sinx$ is $2\pi$ as we all know.
Here x is multiplied by k. so to find the period of $sinkx$ we have to divide the period of $sinx$ by $\left| k \right|$ i.e. $2\pi$ should be divided by $\left| k \right|$ .
Hence the period of $sinkx$ is $\dfrac{{2\pi }}{{\left| k \right|}}$ .

So, the correct answer is “Option C”.

Note : Here in this solution we have noticed that the period of $sinx$ is divided by $\left| k \right|$ instead of k. Because the period of any function cannot be negative it can be fraction but cant be negative.