Question

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

Answer 1

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]}