Pre-Calculus 12 · Algebra
Trigonometric Identities
A trigonometric identity is an equation true for all values of the variable — not just some. Proving sin²θ + cos²θ = 1 from the unit circle definition is the foundational example. From it flow the double-angle and sum-difference identities. Identity proofs demand algebraic creativity and strategic thinking: transform one side using legal moves until it matches the other.
WHAT STUDENTS WILL LEARN
✓Prove and apply the Pythagorean identities: sin²θ + cos²θ = 1
✓Apply sum, difference, double angle, and related identities
✓Simplify trigonometric expressions using identities
✓Prove trigonometric identities by transforming one side
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