write a sine function that had an amplitude of 4, a midline if 2 and a frequency of 3pi/8

Answer 1

sinx has midline 0

to move it up 2, just add 2

sinx +2

sinx has amplitude 1

to increase the amplitude by 4 fold, just multiply by 4

4sinx + 2

frequency = the inverse of the period

f=1/p

for f = 3pi/8, the period is 8/3pi

just flip the fraction upside down

sinx, 4sinx and 4sinx+2 all have period = 2pi

to reduce the period to 8/3pi calculate the coefficient of x with

8/3pi = 2pi/C, solve for C

C = 3pi^2/4

thus

f(x) = 4sin(3xpi^2/4) + 2

is a sine function with amplitude 4, midline 2, and frequency 3pi/8