Respuesta :
Recall that the general shape of a sine function is of the form
[tex]A\sin (Bx-C)+D[/tex]where A is the amplitude of the function, D is the midline, the number C/B is the phase shift and the number is 2*pi/B is the period of the function.
In our case, we are told that A=4 and D=3. Since we are told a value of the period, but nothing about the phase shift, we will assume that the phase shift is 0. Then, we have the following equations
[tex]\frac{C}{B}=0[/tex]and
[tex]\frac{2\cdot\pi}{B}=\frac{8}{5}[/tex]Form the first equation, we can determine that C=0.
From the last equation, we can multiply both sides by 5*B, so we get
[tex]8\cdot B=5\cdot2\cdot\pi=10\cdot\pi[/tex]Finally, we divide both sides by 8, so we get
[tex]B=\frac{10\cdot\pi}{8}=\frac{5\cdot\pi}{4}[/tex]So, we end up with the following formula
[tex]4\cdot\sin (\frac{5\cdot\pi}{4}x)+3[/tex]