Trigonometry

Learn Trigonometry

From right triangles to the unit circle to identities. This is the bridge that carries you into calculus.

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Free to start · adaptive placement finds your level · reviews timed to your own forgetting.

What you'll learn

35 lessons in Trigonometry

Right-triangle trig (SOHCAHTOA)The unit circleGraphs of sin and cosTrig identitiesLaw of sinesLaw of cosinesInverse trig & their domainsSum & difference formulasDouble-angle formulasHalf-angle formulasGraphs of tan, sec, csc, cotSolving trig equationsArea of triangle via trigTrig form of complex numbersDe Moivre's theoremRoots of unityProving trig identitiesLimit $\sin x / x \to 1$ (geometric proof)Spherical trigonometry previewHyperbolic functionsPolar curvesSolving triangles: law of tangents & half-angleTaylor series of sine & cosineGregory's series & the Leibniz formula for πSpherical trigonometryProduct-to-sum & sum-to-productHarmonic addition: a·sin + b·cosThe tangent half-angle substitutionChebyshev polynomialsEuler's formula & trig identitiesPower-reduction & multiple-angle expansionSimple harmonic motion & sinusoidal modelingFourier series (introduction)The navigator's trig functionsThe Gudermannian: circular meets hyperbolic without i
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the day its model predicts you would forget it. A short placement check finds what you already know, so you start Trigonometry exactly where it's useful.

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