How do you graph # y=-3/4sin(3/4x)#?

1 Answer
Feb 15, 2018

Answer:

Since the question is asking how, look at the Explanation section please.

Explanation:

First, look at the general sinusoidal function:

#a*sin(bx+c)+d#

Amplitude = #a#
Period = #(2pi)/b#
Horizontal Phase Shift = #c/b#
Vertical Phase Shift = #d#

So what this function differs from #sin(x)# is the amplitude and period, because the horizontal and vertical phase shifts are both #0#.

The period is #(2pi)/(3/4)# or #(8)/3pi#. So every #(8)/3pi# the function repeats itself.

Because the amplitude is negative we have to flip the function around the #x# axis. And instead of reaching 1 and -1 for it's maximum and minimum it will reach #3/4# and #-3/4#.

So we now can graph the function:
graph{-3/4sin(3x/4) [-4.73, 5.27, -2.36, 2.64]}