Complete the Lesson 5 Assignment that you saved in your course folder at the beginning of this lesson. Show work to support your answers.

Save your responses in your course folder.

Project Connection

You are now ready to apply your understanding of proving trigonometric identities. Go to Module 5 Project: Pushing the Limits of Vehicle Performance and complete Activity 2: Part 2. Complete any remaining parts of your project.

Save your responses in your course folder. Submit your completed Module 5 Project to your teacher.

Going Beyond

Mathematics is a critical part of human creativity. Like art, mathematics has its own structure, logic, and meaning. Like music, mathematics has harmony and dissonance. Like literature, mathematics has metaphor, ambiguity, and mystery. It has history. Mathematics has a sense of outcome and a feeling of rightness.

Mathematics possesses not only precision, but beauty, especially in the form of an elegant proof. Your experience with this lesson tells you that there are many ways to complete a proof, so what makes one proof ordinary and another elegant?

An elegant proof

• uses a minimum of assumptions
• is unusually succinct
• derives a result in a surprising way
• is based on new and original insights
• can be easily generalized to solve a family of similar problems

Care needs to be taken when reading proofs. It is often possible to follow flawed logic to an absurd conclusion. Consider the following, which claims to prove that 2 = 1.

Comment on the validity of this “proof.”