Question

What is the cosine equation of the function shown? Enter your answer by filling in the boxes. Enter any phase shift as its smallest multiple from the fundamental period.

Answer 1

See the attached figure.

Explanation:

the general equation of cosine function is

f(x) = A cos (x + B) + C

Where:

A is the amplitude

B is the horizontal shift

C is the vertical shift

For the given figure

Maximum = 9, minimum = -1

A = (maximum - minimum)/2 = (9 - -1)/2 = 10/2 = 5

Vertical shift = maximum - A = 9 - 5 = 4

The maximum occurs at x = -π/4, and

for the original function (without shift), the maximum occurs at x = 0

So, the horizontal shift = 0 - (-π/4) = π/4