Adding Trigonometric Functions
Rationale Statement

Trigonometry is an easy subject to connect to the real world, whether it is through angles or functions. Sound waves and additive synthesis are two very important connections to sine waves. If students are to go to the trouble of learning to add trig functions together, they should at least learn about the practical implications of it. What chances does a student have of remembering anything about interference or additive properties of sine waves if there is no tangible explanation for why we would even care about such a thing?

The NCTM standards that are addressed in this lesson plan include:

• Algebra & Functions - students are learning to further manipulate sine functions, and looking for patterns in the additions.
• Geometry - sine waves are rooted in geometric principle
• Problem Solving - students must find a way to add functions when they cannot group like terms.
• Communication - students must be able to express their ideas both verbally and on paper.
• Connections - by applying the addition of sine waves to sound, there are connections to physics and to music.