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

1 Answer
Feb 15, 2018

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]}