Question

Identify the sine function with the given attributes.

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

Answer 1

Last option

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

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.

`(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`

`(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