What is the period of y=sin (3x)

The new period is 2/3 π.

The period of the two elementary trig functions, sin (x) and cos (x) is 2π.

If we multiply the input variable by a constant has the effect of stretching or contracting the period. If the constant, c>1 then the period is stretched, if c<1 then the period is contracted.

We can see what change has been made to the period, T, by solving the equation:

cT=2π

What we are doing here is checking what new number, T, will effectively input the old period, 2π, to the function in light of the constant. So for our givens:

3T=2π

T=2/3 π

Other method to solve this;

sin3 x = sin (3x+2π) = sin [3 (x + 2π / 3) ] = sin3 x

This means "after the arc rotating three time of (x + (2 π/3)), sin 3x comes back to its initial value"

So, the period of sin 3x is 2π / 3 or 2/3 π.