Question

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

Answer 1

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".