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

Feb 15, 2018

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

#### Explanation:

First, look at the general sinusoidal function:

$a \cdot \sin \left(b x + c\right) + d$

Amplitude = $a$
Period = $\frac{2 \pi}{b}$
Horizontal Phase Shift = $\frac{c}{b}$
Vertical Phase Shift = $d$

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

The period is $\frac{2 \pi}{\frac{3}{4}}$ or $\frac{8}{3} \pi$. So every $\frac{8}{3} \pi$ 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 $\frac{3}{4}$ and $- \frac{3}{4}$.

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