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

Trigonometric Identities, Sum and Difference Formulas and Applications


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.

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