Trigonometry Lessons

Master the unit circle — learn exact coordinates for every special angle, all six trig function values, and how to use the circle to solve any trig problem.

Understand and apply a² + b² = c² for right triangles. Includes proofs, worked examples, Pythagorean triples, and real-world applications.

The essential mnemonic for right triangle trig. Learn what SOH-CAH-TOA means, how to pick the right ratio, and solve for missing sides and angles.

Deep dive into the three primary trig functions — their definitions, graphs, periods, amplitudes, and how they relate to the unit circle.

Learn arcsin, arccos, and arctan — how to find angles when you know the ratio. Covers domains, ranges, notation, and common pitfalls.

Solve any triangle with the Law of Sines: a/sin A = b/sin B = c/sin C. Covers the ambiguous case (SSA), worked examples, and proofs.

Generalize the Pythagorean theorem to any triangle. Learn c² = a² + b² − 2ab·cos C with worked examples for SSS and SAS triangles.

Master the essential trig identities — Pythagorean, reciprocal, quotient, co-function, and even-odd identities with proofs and examples.

Derive and apply sin(2θ), cos(2θ), and tan(2θ). Includes half-angle formulas, power-reducing identities, and calculus applications.

The foundation of trigonometry — learn how sine, cosine, and tangent are defined using the sides of a right triangle with step-by-step examples.

Apply trig to real-world height and distance problems. Learn the difference between elevation and depression angles with illustrated examples.

Understand why radians exist, how to convert between radians and degrees, and why calculus and physics prefer radians over degrees.

See how trig powers real physics — vector decomposition, projectile motion, forces on inclines, simple harmonic motion, and wave equations.

Systematic methods for solving equations like sin(x) = 0.5 and 2cos²(x) − 1 = 0. Learn general solutions, factoring, and substitution techniques.

Classify triangles by sides and angles — equilateral, isosceles, scalene, acute, right, obtuse. Learn angle sum, exterior angles, and area formulas.