Answer:
Original equation:
y = a sin(b(θ -c)) + d
a = vertical dilation (stretch) of the amplitude
b = horizontal compression (shrink) of the period
c = horizontal shift (left/right)
d = vertical shift (up/down)
Your function is:
y = 3 sin(3θ + π) - 2
First, put it into the general from by factoring out the three in the argument of the sine:
y = 3 sin(3(θ + π/3)) - 2
a = vertical (amplitude) dilation = 3
b = horizontal (period) compression = 2π/period = 3
c = horizontal shift = π/3 to the left
d = vertical shift = -2
