find an equation of a sinusoidal function that has minimum at the point (2,1) has a period of 8 and an amplitude of 3

Question

find an equation of a sinusoidal function that has minimum at the point (2,1) has a period of 8 and an amplitude of 3

Answer 1

amplitude 3, period = 8 = 2pi/B, B= 2pi/8= pi/4

minimum point (2,1)

Asin(Bx + C) + D

Asin((2pi/8)x + C) + D

A=3 D=4, C=pi

3sin(pix/4 + pi) + 4