Question

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

Answer 1

Answer:

Step-by-step 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 $period=\frac{2\pi}{B}$,

C is used to find the phase shift in the formula $ps=\frac{C}{B}$,

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:

$\frac{3\pi}{2} =\frac{2\pi}{B}$ and we solve for B by cross multiplying:

3πB = 4π and

$B=\frac{4\pi}{3\pi}$ so

$B = \frac{4}{3}$ so the function is

$y=4sin(\frac{4}{3}x)+5$