# How do you graph two complete cycles of y=1/2sint?

Jul 31, 2018

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#### Explanation:

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Create a data table for the Parent function color(red)(y=f(t)=sin(t) as shown below:

Graph the Parent function as shown below:

Next, graph the function: color(red)(y=f(t)=(1/2)*sin(t)

Now, we understand the behavior of the graph

color(red)(y=f(t)=(1/2)*sin(t)

by comparing it to the parent graph.

The question reads draw two complete cycles.

The Period of a trigonometric function is the horizontal length of one complete cycle.

The Sine curve, color(red)(y=sin(t), has a Period of color(blue)(2 pi.

The Sine curve, color(red)(y=(1/2)*sin(t), has also a Period of color(blue)(2 pi.

We need to restrict or place a constraint using an appropriate condition as shown below:

Again, we can compare the restricted graphs of both the parent function and the given function for easy comprehension.

I hope it helps.