Question

What is the cosine equation of the function shown?

Answer 1

Considering the graph, the cosine equation is given by:

$y = 4\cos{\left(x - \frac{\pi}{4}\right)} - 8$

What is a cosine function?

It is modeled by:

$y = A\cos{Bx + C} + D$

In which:

• The amplitude is 2A.

• The period is $\frac{2\pi}{B}$.

• The phase shift is of C.

• The vertical shift is of D.

In this graph:

• The difference between the largest and the smallest value is of 8, hence 2A = 8, A = 4.

• With this amplitude, the function should be between -4 and 4, and it is between -8 and 0, that is, shifted four units down, hence D = -8.

• The period is of $2\pi$, hence B = 1.

• We have that it is 0 at $\frac{\pi}{2}$, while in this graph it is at $\frac{\pi}{4}$, hence the phase shift is given by $C = -\frac{\pi}{4}$.

Thus, the equation is:

$y = 4\cos{\left(x - \frac{\pi}{4}\right)} - 8$

More can be learned about sinusoidal functions at https://brainly.com/question/16818112