Question

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

Answer 1

As below.

Explanation:

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]}