How do you write an equation of a sine function with amplitude 3/4, period 720, no phase shift, vertical displacement 5 units down?

1 Answer
Jun 24, 2018

Answer:

#color(brown)("The equation is "y = (3/4) sin (x/2) - 5#

Explanation:

#"Standard form of sine function is " y = A sin (Bx - C) + D#

#Amplitude = |A|#

#"Period " = (2pi) / |B|#

#"Phase Shift " = -C / B#

#"Vertical Shift " = D#

#"Given ; Amplitude = 3/4, Period "= 720 = 4pi, " Vertical Shift "= -5#
#A = 3/4, (2pi) / B = 4pi " or " B = 1/2, D = -5#

The equation is #y = (3/4) sin (x/2) - 5#

graph{(3/4) sin(x/2) - 5 [-10, 10, -5, 5]}