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

Jun 17, 2018

Explanation:

When graphing trigonometric functions, it's important to identify the amplitude and period from the equation provided. For example, the sine graph:

$y = a \sin \left(b x\right)$

has amplitude $a$ and period $\frac{2 \pi}{b}$.

For the graph, $y = \frac{4}{3} x$ amplitude is 1 and period is given by:
$p = \frac{2 \pi}{\frac{4}{3}}$

$= \frac{3 \pi}{2}$

This means that the graph completes one full oscillation every $\frac{3 \pi}{2}$ units. Since no domain restriction has been provided, the graph continues for infinity (indicated by an arrow) to the left and right of the origin.

To make it easier to graph, split your x-axis into four sections for every oscillation (on the x-axis, up to 1, down to x-axis, down to -1, back up to x-axis).

You can see the graph in the image above.

Hope this helps :)