Creating Equations for Sinsuoidal Functions

In class we learnt how to create equations for Sinusoidal Functions


General Form : f(x) = a sin b (x-c) + d OR f(x) = a cos b (x-c) + d


What you have to do is figure out an equation for the cos function (blue line).






The blue functions equation is y = cosx
In order to make the red sin function look like the blue cos function we would have to shift it to the left.


y = cos x = y = sin (x + π/2) would be one way to show this.


y = -sin (x - π/2) would be another way




The black line represents the cos function which we will be finding the three equations for.
The first step to finding an equation for this function is to check if there is any up or down shifting (d value).

d = 0

Then we would find the amplitude. In this case the amplitude is 5.

a = 5

Next step is to determine the period (b value)

2π / lbl = π
therefore b must = 2 because 2π/2 = π

b=2

Now you have enough to make the 1st equation.

1st equation : y = 5 cos 2x

Now to make your 2nd equation you need to figure out which way you need to shift the function. To make the sin (red line) the same as the cos (black line) you need to shift to left which would be your c value.


2nd equation : y = 5 sin 2 (x + π/4)


For the 3rd equation putting a negative sign in front of the a value flips the function. Now you have to shift to the right.


3rd equation : y = - 5 sin 2 (x - π/4)


And there are the 3 equations.