How do you graph y=-3/4sin(3/4x)y=34sin(34x)?

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)+dasin(bx+c)+d

Amplitude = aa
Period = (2pi)/b2πb
Horizontal Phase Shift = c/bcb
Vertical Phase Shift = dd

So what this function differs from sin(x)sin(x) is the amplitude and period, because the horizontal and vertical phase shifts are both 00.

The period is (2pi)/(3/4)2π34 or (8)/3pi83π. So every (8)/3pi83π the function repeats itself.

Because the amplitude is negative we have to flip the function around the xx axis. And instead of reaching 1 and -1 for it's maximum and minimum it will reach 3/434 and -3/434.

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