Let y=12sin(5x+7)

Question

1. What Is the amplitude
2. what is the period?
3. what is the phase shift?

Answer 1

In general, to find the values you requested from any sine function you want to put the function into the following form:

y=A*sin(B(x+C))+D

in this form, A will be the amplitude of the function. 2π/B will be the period (and the inverse of this is the frequency). C is the phase shift (positive values will push the function in the -x direction). D will be the vertical shift, where positive values will push the function in the y direction.

In your case, the result in putting the function in this form is y=12sin(5(x+7/5))+0