Question

Identify the sine function with the given attributes.

Answer 1

Answer:

Last option

$f(t)=sin(\pi(t -3)) + 4$

Step-by-step explanation:

The general sine function has the following form  

$y = Asin(bt-\phi) + k$

Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.  

$\frac{2\pi}{b}$ is the period: time it takes the wave to complete a cycle.

k is the vertical displacement.

$\phi$ phase shift

We know that:

amplitude: 1; period: 2; phase shift: 3; vertical shift: 4

Thus:

$A =1$

$\frac{2\pi}{b}=2$

$b=\pi$

$\phi=3$

$k=4$

Then the function is:

$f(t)=sin(\pi(t -3)) + 4$

The answer is last option