The graph of a sinusoidal function passes through (0,1) has a maximum point at (pi/2,3), & a subsequent maximum point at (7pi/6, 3)

Question

The graph of a sinusoidal function passes through (0,1) has a maximum point at (pi/2,3), & a subsequent maximum point at (7pi/6, 3)

A) determine the amplitude, period, midline, and range of this function

B) determine a sine function with these characteristics

C) determine a codeine function with these characteristics

Answer 1

(pi/2,3),(7pi/6,3) are max of a sine wave which also goes through (0,1)

min is when x =5pi/6

3 is max

h(t)= AsinB(t-C)+D

A=amplitude = (max-,min)/2 =(3--3)/2=3

B = 2pi/period= 2pi/(4pi/6)=3

D=midline=average= (max+min)/2=0

h(0)=1=3sin-3C

sin-3C=1/3

-3C = arcsin(1/3)

C= phase shift = arcsin(1/3)/3=6.49 degrees = 6.49pi/180 = .036pi

h(t) = 3sin3(t-.36pi)

for

h(t) = 3cos3(t-C) just change C by pi/2, all same except for the phase shift

=3cos3(t-.86pi)