Public learning track
Solving Trigonometric Equations and Systems
11th Grade · Math · Open Global Math
8 lessons
Goal
Solve linear, quadratic, multiple-angle, and harmonic trigonometric equations both algebraically and graphically over defined domains.
Featured Diagrams
Finding All Solutions to Trigonometric Equations on the Unit Circle
8 lessons
0 of 8 done
- 1Finding All Solutions to Trigonometric Equations on the Unit CircleUp nextStart
- 2Solving Multiple-Angle Trigonometric EquationsPremiumNot started yet
- 3Solving Trigonometric Equations in Quadratic FormNot started yet
- 4Solving Trigonometric Equations Using Pythagorean SubstitutionsNot started yet
- 5Solving Trigonometric Equations with Addition FormulasNot started yet
- 6Solving Trigonometric Equations Using Double-Angle IdentitiesNot started yet
- 7Solving Trigonometric Equations Using Harmonic Form TransformationNot started yet
- 8Solving Trigonometric Equations GraphicallyNot started yet
Standards Covered
- OGM.12.TRG.4Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Solve trigonometric equations algebraically and graphically over specified intervals, including quadratic forms in trigonometric ratios and multiple-angle equations, applying inverse functions in contextual modeling.
- OGM.12.TRG.3Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Prove and apply trigonometric identities including Pythagorean identities (sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = csc²θ), angle addition/subtraction, double-angle formulas, and express a cos θ + b sin θ in harmonic form R cos(θ ± α) or R sin(θ ± α).
Curriculum Framework
11th Grade · Math · Open Global Math
1
9 lessons
Radian Measure, the Unit Circle, and Small-Angle Approximations
Master radian angle measure, arc length, sector area, exact trigonometric values, and small-angle approximations.
2
8 lessons
Graphs and Transformations of Trigonometric Functions
Analyze, graph, and interpret the primary and reciprocal trigonometric functions under vertical and horizontal transformations.
3
7 lessons
Inverse Trigonometric Functions and Graphs
Understand domain restrictions, graph inverse trigonometric functions, and evaluate compositions of trigonometric and inverse trigonometric functions.
4
8 lessons
Trigonometric Identities and Harmonic Forms
Prove and apply fundamental, Pythagorean, compound-angle, and double-angle identities, and convert linear combinations into harmonic form.
5
8 lessons
Solving Trigonometric Equations and Systems
Solve linear, quadratic, multiple-angle, and harmonic trigonometric equations both algebraically and graphically over defined domains.
6
6 lessons
Periodic Modeling and Trigonometric Applications
Model real-world cyclical and oscillatory phenomena using sinusoidal functions and solve applied contextual problems using inverse trigonometric functions.