Question

I NEED HELP PLEASE, THANKS! :)

Answer 1

Answer: A

Explanation:

The standard form of a cosine equation is: y = A cos (Bx - C) + D where

• Amplitude (A) is the distance from the center to the max
• Period (P) is the length of the function = 2π/B
• Phase Shift is the distance the max is moved from the y-axis = C/B
• Center (D) is the imaginary line between the max and min

Plot the points (see graph below).

A = 28

`(1)/(2)P=6\quad \rightarrow \quad P=12\\\\\\P=(2\pi)/(B)\qquad \rightarrow \qquad 12=(2\pi)/(B)\qquad \rightarrow \qquad \large\bold{B=(\pi)/(6)}`

Phase Shift = 7 = C/B

`7=(C)/((\pi)/(6))\qquad \rightarrow \qquad \large\bold{C=(7\pi)/(6)}`

D = 49

Input the values of A, B, C, and D into the standard form of a cosine equation to get:

`\large\boxed{y=28\cos \bigg((\pi)/(6)x-(7\pi)/(6)\bigg)+49}`