How do you think changes to the function rules of each of the trig functions might affect their graphs?

The period of the parent graphs of sine and cosine is 2 multiplied by pi, which is once around the unit circle. Sometimes in trigonometry, the variable x, not the function, gets multiplied by a constant. This action affects the period of the trig function graph.

For example, f (x) = sin 2x makes the graph repeat itself twice in the same amount of time; in other words, the graph moves twice as fast. Think of it like fast-forwarding a DVD. This figure shows function graphs with various period changes.

Creating period changes on function graphs.

Creating period changes on function graphs.

To find the period of f (x) = sin 2x,

Equation to find the period of a sine function.

and solve for the period. In this case,

The period of a sine function.

Each period of the graph finishes at twice the speed.

You can make the graph of a trig function move faster or slower with different constants:

Step-by-step explanation:

And that is how.