What is the phase shift, vertical displacement with respect to #y=sinx# for the graph #y=-3sin(6x+30^circ)-3#?

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Answer 1 · 2018-05-10T02:20:51

As below.

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

Given equation is #y = -3 sin (6x + 30^@) - 3#

#y = -3 sin (6x + (pi/6)) - 3#

#A = -3, B = 6, C = -(pi)/6, D = -3#

#Amplitude = |A| = 3#

#"Period " = P = (2pi) / |B| = (2pi)/6 = pi/3#

#"Phase Shift " = -C / B = -(pi/6) / 6 = pi/36, " to the right"#

#"Vertical Shift = D = -3, " 3 down"#

#"For y = sin x fumction"#,

#"Phase Shift " = 0, "Vertical Shift " = 0#

#:. Phase Shift w.r.t. " y = sin x " is " pi/3 to the right.

#"Vertical displacement w.r.t. " y = sin x " is " -3 " or 3 units down"#

graph{-3sin(6x+ 30) - 3 [-10, 10, -5, 5]}