If you play a guitar this might be interesting...
Key Terms: Trigonometric, Frequency, Coordinate Plane.
Purpose: To explain how sound waves determine the shape of chords on a guitar.
IntroductionSound waves are represented by an oscillating curve. They can be approximated by trigonometric functions. The sound produced by each note on a guitar produces a frequency that can be graphed in a coordinate plane.

Activity
The period of a sine curve is the length across the axis it takes to complete a full cycle.
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Analyze the period of each equation.

Write the period for each equation.

Analyze the graph of each equation again.

Looking at the red equation with the longest period, we can see that it completes a full cycle at x=6 and x=12. It also completes a full cycle at x=18,24,30... This is because the period of the red equation is 6.

The period of the blue equation is 4. Write a few multiples of the period.

The period of the green equations is 3. Write a few multiples of the period.

Compare the multiples of each equation. Write the lowest common multiple of all three equations.

What do you notice about the graph at this point on the x-axis?
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Reflection
A guitar chord is formed by playing the 1st, 3rd, and 5th note in a scale. Let's say that the red equation represents the 1st note, the blue represents the 3nd note, and the green represents the 5th note. Make a conjecture about how this parallels what happens on a guitar.