Question

I need help PLEASE !!!! Write a cosine function that has an amplitude of 2, a midline of 4 and a period of 4.

Answer 1

`\mathbf{y = 2cos ( (\pi)/(2)(x - 0) + 4}`

Explanation:

The standardized cosine function is ;

`\mathbf{y = Acos (Bx + C) +D}`

Amplitude |A| = 2

Period
`(2 \pi)/(B )= 4`

2π = 4B

`B = (2 \pi)/(4)`

`B = (\pi)/(2)`

Midline y = 4; D = 4

Phase shift; since no phase shift is given; then C = 0

The cosine function:
`\mathbf{y = 2cos ( (\pi)/(2)(x - 0) + 4}`