Question

How do you find the period and amplitude of `y=1/4sin(2pix)`?

Answer 1

The period is `T=1`. The amplitude is `=1/4`

Explanation:

The period `T` of a periodic function `f(x)` is defined by

`f(x)=f(x+T)`

Here,

`f(x)=1/4sin(2pix)`............................`(1)`

Therefore,

`f(x+T)=1/4sin2pi(x+T)`

`=1/2sin(2pix+2piT)`

`=1/4sin(2pix)cos(2piT)+1/4cos(2pix)sin(2piT)`...........................`(2)`

Comparing equations `(1)` and `(2)`

`{(cos2piT=1),(sin2piT=0):}`

`=>`, `2piT=2pi`

The period is `T=1`

For the sine function

`-1<=sinx<=1`

`-1/4<=1/4sinx<=1/4`

`-1/4<=1/4sin2pix<=1/4`

The amplitude is `=1/4`

graph{1/4sin(2pix) [-0.587, 2.113, -0.696, 0.654]}