Description

At this point, we turn our attention to various formulas and identities between the 6 trigonometric functions. We start by completely exploring many problems involving identities. Next, we explore trigonometric formulas such as the sum and difference formulas; double angle and half angle formulas and the product-to-sum and sum-to product formulas and their applications.

Sections of this topic include:

1. Identities

   We begin this section with an exploration of how to veriy (or prove) identities. Being that this is a challenging concept, many videos have been produced. Groups within this section include verifying identities; showing an equation is not an identity; using trigonometric substitutions with Sin; using trigonometric substitutions with tan, using trigonometric substitutions with sec.

2. Solving Trigonometric Equations

   Applying our knowledge of Trigonometry to solving equations, we explore various techniques of solving Trigonometric Equations. Groups in this section include solving trigonometric equations with solutions in an interval; finding all solutions to a trigonometric equation.

3. Sum and Difference Formulas

   We now are ready to explore formulas for Trigonometric functions. Groups in this sectioni include using the Co-Function Theorem; using the sum and difference formulas to find exact values; using the sum and idfference formulas to write sine or cosine with a single angle; using the sum and differences formulas to find exact values using other trigonometric ratios; using the sum and difference formulas to verify reduction formulas; and using the sum and difference formulas to verify identities.

    

4. Double and Half Angle Formulas

   Continuing our study of formulas, we now investigate both double and half angle formulas. Groups within this section include finding exact values of double angle formulas using given information; finding exact values of half angle formulas using given information; using half angle formulas to find exact trigonometric values for angles; verifying identities; using power reducing formulas; using double angle formulas to solve equations.

5. Product-To-Sum and Sum-To-Product Formulas

   Our last exploration of formulas leads us to Product-To-Sum and Sum-To-Product formulas. Groups in this section include using the Product-To-Sum or the Sum-To-Product formulas; verifiying identities; and expressing an Algebraic product as a sum.