Creating Equations for Sinusoidal Functions

On Wednesday we learned how to find out what the equation of the graph is.

The equation should consist of f(x)=asinb(x-c)+d or f(x)=acosb(x-c)+d

a=Amplitude
b=affects the period , Period= 2π/b
c=horizontal shift
d=vertical shift

To find the amplitude of your equation, from the middle of your graphed function you count up or down until you reach where the point has stopped.

To find your b value you must find the period first! By counting from one period of the function to the other. Then you must solve for b in the equation 2π/b= period.

To find the horizontal shift you would use the original sin or cos and see how many points it moves horizontally. And remember (x-#) means that the # moves right.

The d value is very easy to figure out. You just find the middle of the function and see what point the y axis is. But make sure you see how many points it moves vertically from whichever you use wether it be sin or cos.


Here is an example below on how to find out the different values to create a equation for a sinusoidal function: