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# Chapter 10.4 - Exercises

# Trigonometric Identities, Sum and Difference Formulas and Applications

## Module Overview

**TMM 002 PRECALCULUS **(Revised March 21, 2017)

**4. Equivalencies**:

** 4c**. Become fluent with conversions using traditional equivalency families.*

Sample Tasks:

- The student can prove trigonometric identies.
- The student solves trigonometric equations.

# Section 1: Trigonometric Identities and Formulas

Formulas introduced in this chapter seem to be many but all of them are derived from the fundamental identities and the sum/difference formulas. It would be very helpful for students if they strive to derive the double-angle, half-angle, etc., formulas from the sum/difference formulas. Proving other identities is a challenge but is an important exercise. This can be supplemented by assigning problems of computing trigonometric ratios of certain angles. For example, finding the value of COS(3.75°) which requires repeated use of half-angle formula or finding \(\sin^{4}(\pi/16)\) which requires power-reduction.

In this module, we use the fundamental identities to derive important formulas for the six trigonometric functions which are quite useful in calculus.

**Review: **Fundamental trigonometric identities and the Pythagorean Theorem

**Learning Objectives**:

- Even – Odd Identitites
- Cofunction Identities
- Sum and Difference Formulas
- Double Angle Formulas
- Half-Angle Formulas
- Power Reduction formulas
- Product to Sum and Sum to Product Formulas