How do you graph y= 3sin2x ?

Aug 24, 2015

Find the amplitude and period.

Explanation:

The general form for a sin function is;

$y = A \sin \left(B x + C\right) + D$

Each constant, $A$, $B$, $C$, and $D$ tells us something about the function. $C$ and $D$ tell us the horizontal and vertical shift of the function. In the case of $y = 3 \sin \left(2 x\right)$ both are zero, so the graph isn't translated up or to the side.

$A$ is the amplitude, so $A = 3$ tells us that the graph is going to fluctuate between $3$ and $- 3$.

Lastly, $B$ is the frequency. $B = 2$ tells us that there will be $2$ full waves between $0$ and $2 \pi$. A more useful number would be the period, $p$.

$p = \frac{2 \pi}{B} = \frac{\cancel{2} \pi}{\cancel{2}} = \pi$

So we know that the wave is going to repeat every $\pi$ radians.

A sin wave starts at $0$, goes to $A$, back to $0$, then to $- A$.