Question

How do you find the amplitude, phase shift and period of `y=2/3 sin πx`?

Answer 1

The general formula for `sinx` is:

`y = Asin(kx + phi) + h`
where:
`A` is amplitude
`k prop 1/T`, i.e. if `k = 1`, then `T = 2pi`, but if `k = 2`, then the period is `pi`
`phi` is the phase shift left or right (left is positive, right is negative)
`h` is the vertical shift (up is positive, down is negative)

From this you should be able to identify that:

`A = 2/3`
`k = pi`
`phi = 0`
`h = 0`

Thus, with `k = pi`,
`pi*1/T = 1/(2pi)*pi = 1/2 -> T = 2 "rad"`