Write an equation of the cosine function with the given amplitude, period, phase shift, and vertical shift. amplitude: 2, period = π, phase shift = (–1/8)π , vertical shift = –2

Step-by-step explanation:

Recall the trigonometric definitions for the geometrical characteristics given to you:

For a General Harmonic function of the type:

we define:

|A| = Amplitude of the function

Period of the function =

Phase shift =

vertical shift = D

Therefore we can construct a function that includes the appropriate geometric characteristics requested by using:

A = 2

To find B we use the definition of period, and what value we want it to have:

To find C we use the definition of phase shift  and the value we want it to have (also using the value for B we found in the step above):

and finally, D = -2

Therefore the function will look like: