Question

ANOTHER MATH QUESTION!! Please help me do this question and explain how you answer it thank you!!!

Answer 1

`y=8\cos \left((1)/(2)x+\pi\right)+2`

Explanation:

The equation of cosine function will be

`y=a\cos (kx+b)+c`

Find
`a:`

The minimum y is
`y_(min)=-6,` the maximum y is
`y_(max)=10,` so

`a=(1)/(2)\cdot |-6-10|=(1)/(2)\cdot 16=8`

Find
`k:`

The period of the function is
`T=4\pi,` so

`T=(2\pi )/(k)\Rightarrow k=(2\pi )/(4\pi )=(1)/(2)`

Find
`b:`

At
`x=0,\ y=y_(min)=-6`

Function
`y=\cos x` at
`x=0` has the value
`y=y_(max)=1,` so
`b=\pi` [translate by one-fourth of the period]

Find
`c:`

The graph has the midline
`y=(10-6)/(2)=2,` so
`c=2.`

Hence,

`y=8\cos \left((1)/(2)x+\pi\right)+2`