What is the period of the function #y=3 sin(2x)#?

1 Answer
Shell
Dec 29, 2016

The period is #pi#.

Explanation:

Given a trig function in the form #y=Asin(Bx-C)+D#.

the period is equal to #(2pi)/B#.

In this example, #y=3sincolor(red)2x#, #B=color(red)2#

The period is equal to #(2pi)/color(red)2 =pi#.

Another way to think of this is by examing the function #y=sinx#, which has a period of #2pi#. In other words, once complete cyle of sin is #2pi# "long".

In comparison, #y=sincolor(red)2x# has a period of #pi#, and #color(red)2# complete cycles "fit" within #2pi#, making one cycle #pi# "long".

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