Question

How do you find the period, amplitude and sketch `y=2+1/10cos60pix`?

Answer 1

See below.

Explanation:

Period:

The period of `cosx=2pi`

Multiplying `x` by `60pi` causes a compression by a factor of `1/(60pi)`

So period is `1/(60pi)*2pi=1/30` radians

The amplitude of `cosx = 1`

Multiply by `1/10` causes a reduction by a factor of 10.

So `1/10*1=1/10`

This is increased by 2, because the function has had 2 added to it, which translates the curve in the positive y direction by 2 units.

So amplitude is:

`1/10+2=21/10=2.1`

The stretch is a compression in this case by a factor of `1/(60pi)`

`:.`

Period is `color(blue)(1/30)` radians

Amplitude is `color(blue)(2.1)`

Stretch is `color(blue)(1/(60pi))`

Plots: