Material Type:
Ohio Open Ed Collaborative
Mathematics, Tmm0022
Creative Commons Attribution-NonCommercial 4.0
Media Formats:

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