Question

Write a sine function with the given amplitude, period, phase shift, and vertical shift.

amplitude: 2; period: pi; phase shift: -1/8 pi; vertical shift: 3

Answer 1

`y = 2 sin ((2x- 1)/(16 \pi) ) - 1`

Explanation:

We know that the standard form of equation for the sine function is given by:

`y = Asin(Bx-C)` where
`A` is amplitude, period is
`(2\pi )/(B)` and the phase shift is equal to
`Bx-C` set to zero.
`C` is then obtained by this equation.

Here in this problem: A is equal to 2, period=2π/B=2π/2=π, where B is equal to 2 and the phase shift is equal to 2x - 1/16 pi = 0.

`y = 2 sin (\frac { 2 x - 1 } { 16 \pi} ) - 1`