Question

Write a sine function that has a midline of 5, an amplitude of 4 and a period of 3pi/2

Answer 1

Explanation:

The standard form for this function is

y = Asin(Bx - C) + D where

A is the amplitude,

B is used to find the period in the formula
`period=(2\pi)/(B)`,

C is used to find the phase shift in the formula
`ps=(C)/(B)`,

and D is the midline which either moves the function up or down from its natural midline of 0.

We have no given phase shift, so there is no C value. The amplitude is easy; we just fill in A as 4. The period is another story:

`(3\pi)/(2) =(2\pi)/(B)` and we solve for B by cross multiplying:

3πB = 4π and

`B=(4\pi)/(3\pi)` so

`B = (4)/(3)` so the function is

`y=4sin((4)/(3)x)+5`