Question

1. Complete the general form of the equation of a sinusoidal function having an amplitude of 1, a period of π/2 , and a vertical shift up 3 units.
Y=_________________
2. Complete the general form of the equation of a sinusoidal function having an amplitude of 4, a period of π , and a phase shift to the right 2 units.
Y=_________________
3. Describe the transformations on the sine curve to get the graph of y = 3sin(4x + π ). Include a sketch of the graph as part of your answer.

Answer 1

1. Sinusoidal function
Amplitude: A=1
Period: P=π/2
Vertical shift up (+): VS=3
Phase shift: PS=0

y=a sin (bx+c)+d

A=a→a=1
P=2π/b→π/2=2π/b→bπ/2=2π→b=2(2π)/π→b=4
PS=-c/b=0→-c/4=0→-c=4(0)→-c=0→c=0
VS=d→d=3

y=1 sin (4x+0)+3→y=sin(4x)+3

2. Sinusoidal function
Amplitude: A=4
Period: P=π
Vertical shift up (+): VS=0
Phase shift to the right (+): PS=2

y=a sin (bx+c)+d

A=a→a=4
P=2π/b→π=2π/b→bπ=2π→b=2π/π→b=2
PS=-c/b=2→-c/2=2→-c=2(2)→-c=4→c=-4
VS=d→d=0

y=4 sin (2x+(-4))+0→y=4 sin(2x-4)

3. y=3 sin(4x+π)=3 sin [ 4(4x/4+π/4]→y=3 sin [4(x+π/4)]
Phase Shift to the left π/4 units
Horizontal compression by a factor of 1/4
Vertical stretch by a factor of 3