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.
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