Question

How do you find the period and amplitude of `y=2/3cos((pix)/10)`?

Answer 1

amplitude is 2/3
period is 20

Explanation:

`y=alpha*cos(x)` period is given as `(2pi)` and amplitude is `alpha`
for `y=cos(ax)`, period is given as `(2pi)/a`
here, y=`(2/3)cos(pi/10)x`
so period is `(2pi)/(((pi)/10))=20`

also, amplitude is `2/3`, because the maximum deviation of curve from the mean is `2/3` at cos`((pix)/10)` = 1

graph{(2/3)cos((pix)/10)[-10, 10, -5, 5]}