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 [tex]period=\frac{2\pi}{B}[/tex],
C is used to find the phase shift in the formula [tex]ps=\frac{C}{B}[/tex],
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:
[tex]\frac{3\pi}{2} =\frac{2\pi}{B}[/tex] and we solve for B by cross multiplying:
3πB = 4π and
[tex]B=\frac{4\pi}{3\pi}[/tex] so
[tex]B = \frac{4}{3}[/tex] so the function is
[tex]y=4sin(\frac{4}{3}x)+5[/tex]
