For b > 0, the graph of y = sin bx will have a period of?

We will use the concept of periodicity in order to find the required period.

Answer: For b > 0, the graph of y = sin bx will have a period of 2π/b.

Let us see how we will use the concept of periodicity in order to find the required period.

Explanation:

We know that the period of y = sin x is 2π.

Due to the presence of coefficient b in x and since b > 0, y will attain the value b times before x = π/4, π/2, π, 2π, respectively.

The variable b gives the number of cycles between 0 and 2π. Higher b gives higher frequency (and lower period).

Hence, for b > 0, the graph of y = sin bx will have a period of 2π/b.