Question

What is the period of the graph of the equation y = a sin bx?

Answer 1

T=2π/|b|. The period of an equation of the form y = a sin bx is T=2π/|b|.

In mathematics the curve that graphically represents the sine function and also that function itself is called sinusoid or sinusoid. It is a curve that describes a repetitive and smooth oscillation. It can be represented as y(x) = a sin (ωx+φ) where a is the amplitude, ω is the angular velocity with ω=2πf, (ωx+φ) is the oscillation phase, and φ the initial phase.

The period T of the sin function is T=1/f, from the equation ω=2πf we can clear f and substitute in T=1/f.

f=ω/2π

Substituting in T=1/f:

T=1/ω/2π -------> T = 2π/ω

For the example y = a sin bx, we have that a is the amplitude, b is ω and the initial phase φ = 0. So, we have that the period T of the function a sin bx is:

T=2π/|b|