Thread: Writing a Sin and Cos Function Equation

A sine function has a max value of 7, min value of -1. Phase shift is 3pi/4 to the left. Period is pi/2

Write an equation for the function and then graph the function..

Ok, I did this question, and my equation was something like this:

y=4sin(4(x+3pi/4))

However, in the back of the book. The answer is y=4sin(4(x+3pi/4))+3

The k value in the equation? I am not sure how to get this k value.

How would I figure this out? Am I wrong or is it wrong in the back?

thank you

Hi

Your answer is not correct because your minimum is -4 and your maximum is 4

The mean value is (7+(-1))/2 = 3 = number to be added to sine

The amplitude is max-mean = mean-min = 7 - 3 = 3 - (-1) = 4 = factor of sine

The period is pi/2 therefore sine is applied to (4x + phi) because
sin(4(x+pi/2) + phi) = sin(4x + 2pi + phi) = sin(4x + phi)

The phase shift is phi = 3pi/4

The function is therefore : 3 + 4sin(4x+3pi/4)