How do you graph and list the amplitude, period, phase shift for #y=-3sin(2x)-3#?

1 Answer
Sep 15, 2016

Answer:

Amplitude = 3; period = #pi#, phase shift = 0; vertical shift = #-3#.

Explanation:

In general symbols,

for the oscillation y = a sin (b x +c ) + d,

Amplitude = #|a|#

period = #2/bpi#

Phase shift = #-c/b

Vertical shift = d.

Here, for #y = -3 sin (2x) - 3,

Amplitude = 3; period = #pi#, phase shift = 0; vertical shift = #-3#.

For the graph, this graph is topsy turvy ( due to negative sign ) of the

graph for

#y = 3sin 2x -3#

The axis of the wave is #y = -3#..

One half wave is from (0, -3) to (pi/2, -3),.

with the bisector nadir at (pi/4, -6).

The next half, for one full wave, is from (pi/2, -3) to (pi, -3), with

zenith ( crest ) at (3/4pi, 0).

Now, you can make it for this Table: I lack facility for making it, for

you.

#(x, y): (0, -3) (pi/4, -6) (pi/2, -3) (3/4pi, 0) (pi, -3)#

Either side outside, it is lateral (horizontal ) successive movement

of this single wave, through the period #pi#. .