Find a sinusoidal function with the following four attributes:

Question

(1) amplitude is 16, (2) period is 9, (3) midline is y=33 , and (4) f(3)=49 .

Answer 1

f(x) = y = Asin(B(x)-C) + D

where A=Amplitude = 16 = (max-min)/2

period = 2pi/B, B = 2pi/period = 2pi/9

C = phase shift = pi/6 = horizontal shift

D = midline = average = (max+min)/2=33

plug in the values

f(3) = 49 = 16sin(2pi/9)(3) - C) + 33

16sin(2pi/3 -C) =16

sin(2pi/3 -C) = 1

2pi/3 -C = arcsin1 = pi/2

C = 2pi/3 -pi/2 = pi/6

f(x) = 16sin(2pix/9 - pi/6) +33 is the sinusoidal function