Question

Question #7b467

Answer 1

Given: `y = Asin(Bx+C)+D`

The amplitude is A
The period is `P=(2pi)/B`
The phase shift is `theta= -C/B`
The vertical shift is D

Explanation:

Start with

`y = Asin(Bx+C)+D`

We are given the amplitude, `A = 3`:

`y = 3sin(Bx+C)+D`

We are given that the period `P = pi/6` and we know that `B = (2pi)/P`

`B = (2pi)/(pi/6)`

`B = 12`

`y = 3sin(12x+C)+D`

We are not given a vertical shift, therefore, we shall assume that `D=0`:

`y = 3sin(12x+C)`

Use the point `(1/6,0)` to determine the value of C:

`0 = 3sin(12(1/6)+C)`

`12(1/6)+C= 0`

`C = -2`

The equation of the curve is:

`y = 3sin(12x-2)`