Write the equation of a sine function that has the following characteristics. Amplitude: 5 Period: 6pi Phase Shift: 1/5

Question

Amplitude: 5

Period: 6pi

Phase Shift: 1/5

Thanks so much in advance!

Answer 1

Hi, Mann!

For this problem, the key is to use the generalized sine function formula:

y = A sin(B(x+C)) + D, where

Amplitude is given by A

Period is given by 2pi/B

Horizontal phase shift is given by C (positive C indicates a shift to the left)

Vertical shift is given by D

We are given that the amplitude is 5 --> A = 5

Next, we are given that the period is 6pi --> 6pi = 2pi/B. Solving for B yields B = 1/3

Finally, we are given that we have a phase shift of 1/5 (assumed to the left) --> C = 1/5

(Please note that if you are told that the phase shift is to the right, then this value of C would need to be negative.)

We are also not given any vertical shifts, so we can assume D = 0.

We then can substitute in these values of A, B, C, and D into our generalized equation, which gives us the formula:

y = 5sin((1/3) (x+(1/5)))

I hope that this explanation is helpful, and please don't hesitate to reach out if you have additional questions!