Question 1202328
<font color=black size=3>
Answer: <font color=red size=4>y = -8cos(2x)+5</font>
This is when we are in degree mode.
Other answers are possible.


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Explanation:


The template for cosine is
y = A*cos(B(x-C))+D


where,
|A| = amplitude
B = used to find the period
C = phase shift
D = midline


|A| = 8 leads to either A = 8 or A = -8
Let's go with A = -8 because A = 8 will make x = 0 lead to a max, when we want x = 0 to lead to a min instead.


"period of 180" seems to imply your teacher wants things in degree mode (rather than radians).
T = 180 = period
B = 360/T
B = 360/180
B = 2


To make things simple, I'll have the phase shift be set to C = 0.


One minimum point is located at (0,-3)
The smallest y output possible is y = -3
Go up 8 units, the amplitude amount, to arrive at y = -3+8 = 5 which is the midline
Therefore, D = 5



Summary:
A = -8
B = 2
C = 0
D = 5


y = A*cos(B(x-C))+D
y = -8*cos(2(x-0))+5
<font color=red>y = -8cos(2x)+5</font>


Graph
<a href="https://www.desmos.com/calculator/gigkk7becm">https://www.desmos.com/calculator/gigkk7becm</a>
GeoGebra is another graphing option I recommend.