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# Help graphing cosine function!

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The graph of a cosine function has an amplitude of 5, a vertical shift of −1, and a period of 4. These are the only transformations of the parent function. Use the Sine tool to graph the function. The first point must be on the midline, and the second point must be a maximum or minimum value on the graph closest to the first point. The graph of a cosine function has an amplitude of 5, a vertical shift of −1, and a period of 4. These are the only transformations of the parent function. Use the Sine tool to graph the function. The first point must be on the midline, and the second point must be a maximum or minimum value on the graph closest to the first point.

Jun 9, 2022

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We have this  form

y = A cos ( Bx)  +  C

A = the amplitude =  5

B =  (2pi) /period =   (2 pi)  / 4 =   pi /2

C =  the vertical shift

The midline    is  y =  -1

To find  the   x  value of  the first  point we are  looking for we can solve this

-1   = 5 cos  (  [ pi/2] *x ]  - 1

0  = 5 cos  (pi/2 * x)     divide by 5

0  =  cos (pi/2 * x)

We can just let  x = 1  since cos (pi/2)  = 0

The function  is   y  =5 cos ( pi/2  * x)    -  1

Here's the graph  :  https://www.desmos.com/calculator/so6a13kqrw   Jun 9, 2022
edited by CPhill  Jun 9, 2022