Question

How do you sketch the graph of `y=sin (x/2)`?

Answer 1

Use the parent function `y = sin x` with period `= 4pi` instead of `2pi`

Explanation:

Parent function is `y = sin x` with period = `2 pi`

`x/2 = 1/2x` changes the period. Period `= (2pi)/(1/2) = 4pi`

Divide the period into `4` sections:
`x = 0, x = pi, x = 2 pi, x = 3pi, x = 4pi`

`(0,0)` is an `x`-intercept
`(pi, 1)~~(3.14, 1)` is a maximum
`(2pi, 0)~~(9.4, 0)` is an `x`-intercept
`(3pi, -1)~~(9.4, -1)` is a minimum
`(4pi, 0)~~(12.6, 0)` is an `x`-intercept

graph{sin (x/2) [-10, 10, -5.21, 5.21]}