Question

Write an equation of the cosine function with amplitude 2 and period 6π.

Answer 1

The general equation of cosine function is:

`y=a\cos (bx+c)+d`

where:

a = amplitude

`(2\pi)/(b)=period`
`(-c)/(b)=horizontal\text{ shift}`

d = vertical shift

In this case, we have no vertical nor horizontal shifts, then:

c = 0

d = 0

The amplitude is 2, then:

a = 2

The period is 6π, then:

`\begin{gathered} (2\pi)/(b)=6\pi \\ 2\pi=6\pi\cdot b \\ (2\pi)/(6\pi)=b \\ (1)/(3)=b \end{gathered}`

Substituting this information into the general equation, we get:

`\begin{gathered} y=2\cos ((1)/(3)x+0)+0 \\ y=2\cos ((1)/(3)x) \end{gathered}`