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Analytic Trigonometric Identities and Harmonic Conversions

12th Grade · Math · Open Global Math

7 lessons

Goal

Construct formal algebraic proofs for fundamental, compound angle, and double angle identities, and convert linear combinations to harmonic forms.

7 lessons
0 of 7 done
  1. Formal Proofs and Reductions of Pythagorean IdentitiesUp next
  2. Evaluating Exact Trigonometric Values Using Compound AnglesNot started yet
  3. Proving Identities Using Addition and Double Angle FormulasNot started yet
  4. Half-Angle and Power-Reducing FormulasNot started yet
  5. Product-to-Sum and Sum-to-Product FormulasYou are here
  6. Converting Linear Combinations to Harmonic Form: R cos(θ ± α) and R sin(θ ± α)Not started yet
  7. Maximum and Minimum Optimization Using Harmonic FormsNot started yet
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Learning standards covered

GlobalOGM.13.TRG.3Open Global Math Standards 2026™ · 12th Grade

Construct proofs of trigonometric identities including Pythagorean ($\\sin^2 \\theta + \\cos^2 \\theta = 1, 1 + \\tan^2 \\theta = \\sec^2 \\theta, 1 + \\cot^2 \\theta = \\csc^2 \\theta$), compound angle, double angle, and harmonic form conversions $R\\cos(\\theta \\pm \\alpha)$ and $R\\sin(\\theta \\pm \\alpha)$; solve trigonometric equations in specified intervals.