Determine the sinusoidal function

Question

A sinusoidal function has a minimum located at

(-1,10), and a maximum located at (3, 22). Determine a possible equation to model this function

using sine as the base function and another possible equation using cosine as the base function.

Answer 1

for points (-1,10) and (3,22)

A=amplitude = half the difference of max and min = (22-10)/2 = 6

C= phase shift = -1 for sine wave

D = midline = 16= min + A

period =2(3--1) = 8

B =frequency= 2pi/period = 2pi/8 = pi/4

f(t) = Asin(B(t+C)+D

f(t) = 6sin((pi/4)(t-1))+16

for cosine wave, phase shift = -3