Writing the Equation of a Function Given the Amplitude and Period
What if you are given the amplitude and period and are asked to write the equation of a function? The following is an example of how that would be done.
Given an amplitude of 5 and a period of 
, write the equation of the cosine function, expressed in terms of x.
You know that the amplitude is equal to A in the general equation f(x) = A cos(kx), so you can write: f(x) = 5 cos(kx).
Now you will need to find k using the given period.
Solve for k by cross-multiplying:
You can now write the final equation:
f(x) = 5 cos(14x)