Question

The graph of a sinusoidal function has a maximum point at (0,8) and then has a minimum point at (5,2). Write the formula of the function, where x is entered in radians.

Answer 1

y = 3 cos(π/5 x) + 5

Explanation:

The amplitude is half the difference of the min and max.

A = (8 − 2) / 2

A = 3

The midline is the average of the min and max.

C = (8 + 2) / 2

C = 5

The difference in the x values of the min and max is half the period.

T/2 = 5 − 0

T = 10

The function is a maximum at x = 0, so use cosine.

y = 3 cos(2π/10 x) + 5

y = 3 cos(π/5 x) + 5