Creating Equations for Sinusoidal Functions

Hi! This is kyle and we learned about how to create equations for sinusoidal functions.

So, these are the things that you need to know first..
a - amplitude
b - |b|
c - horizontal shift
d - vertical shift
because those are the ones the will be going to be plugged in f(x) = a sin b(x - c) + d or f(x) = a cos b(x - c) + d

moving on..

STEPS ON FINDING THE EQUATION FOR SINUSOIDAL FUNCTIONS:
1.) Find the middle axis (d - vertical shift) of the graph. It is the one that determines the up and down shifting of the graph.
2.) Determine the amplitude.
3.) Determine the period. Then, you can now solve for the |b| value.
4.) Identify the type of wave. It is only either sin or cos.
5.) Determine the horizontal shift by counting how many radians it shifted to the left or right.
6.) Create the equation by plugging the a,b,c,d value in f(x) = a sin b(x - c) + d or f(x) = a cos b(x - c) + d