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

1 Answer
JMicheli
Jul 12, 2016

The new period is #2/3 pi#.

Explanation:

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

Multiplying 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 = 2pi#

What we are doing here is checking what new number, #T#, will effectively input the old period, #2pi#, to the function in light of the constant. So for our givens:
#3T = 2pi#
#T = 2/3 pi#

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