Lesson 6.1
Fundamental Identities
An identity holds for all inputs where both sides are defined. Rewrite using sine and cosine, use the Pythagorean identity, and keep original domain exclusions even when an expression simplifies.
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Unit 6
Identities and Trigonometric Equations
Rewriting trigonometric expressions into a form that can be evaluated or solved, and reporting every solution the interval demands.
Lessons and exercises
Lesson 6.2
Angle Sum and Double-Angle Identities
Angle-sum formulas give exact values by combining familiar angles. A double-angle formula is a special case. Substitution should keep the subtraction signs and the quadrant signs of every sine and cosine.
Lesson 6.3
Solving Trigonometric Equations
Use a reference angle and all compatible quadrants, then restrict to the stated interval. Factoring is safer than dividing by a trigonometric expression that might be zero. A general solution includes periodic repeats.
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