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.