Answer:
Last option
[tex]f(t)=sin(\pi(t -3)) + 4[/tex]
Step-by-step explanation:
The general sine function has the following form
[tex]y = Asin(bt-\phi) + k[/tex]
Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.
[tex]\frac{2\pi}{b}[/tex] is the period: time it takes the wave to complete a cycle.
k is the vertical displacement.
[tex]\phi[/tex] phase shift
We know that:
amplitude: 1; period: 2; phase shift: 3; vertical shift: 4
Thus:
[tex]A =1[/tex]
[tex]\frac{2\pi}{b}=2[/tex]
[tex]b=\pi[/tex]
[tex]\phi=3[/tex]
[tex]k=4[/tex]
Then the function is:
[tex]f(t)=sin(\pi(t -3)) + 4[/tex]
The answer is last option
