Question

How do you graph two complete cycles of `y=3sint`?

Answer 1

Using the variable "t" instead of "x" on the horizontal axis,

Explanation:

you plot values for "t" from t = 0 to t = 4pi.

One full cycle of the sine function goes from zero to 2pi, which is approximately 6.2832, so two full cycles will go from x (or t)=0 to x (or t) = 4pi, which is approx. = 12.5664.

In the graph below, 4pi is the point where the graph crosses the x-axis between 10 and 15.
graph{y = 3sin(x) [-0.8, 19.2, -4.94, 5.48]}

This graph is one complete cycle of y = sinx:

graph{y = sinx [-0.486, 6.63, -1.48, 2.226]}
from t = 0 to t = 2*pi.

I think you can click on the graphs to see the coordinates of the main points.