A-level maths / Pure 1 / Trigonometric ratios
Trigonometric ratios
Find lengths and angles, solve triangle problems and understand the repeating graphs.
Choose a lesson or jump to a section. Move each model yourself, keep the written explanation in view and use the optional animations when they help.
- Cosine ruleFind missing sides and angles with the cosine rule. Includes opposite-side labels, bearings, algebraic lengths, triangle inequalities and minimum-length problems.
- Sine rule and ambiguous caseUse the sine rule to find sides and angles. Understand why two triangles may fit the same data, and check zero, one or two possible solutions.
- Triangle areasFind triangle areas using ½ab sin C, including obtuse angles, three given sides, unknown angles, exact values and maximum-area problems.
- Bearings and triangle problemsSolve bearings, elevation and compound-shape problems using trigonometry. Choose the right triangle, transfer shared lengths and test ambiguous positions.
- Sine, cosine and tangent graphsSketch sine, cosine and tangent in degrees. Learn exact landmarks, periods, negative angles, tangent asymptotes and how to read repeated solutions.
- Transforming trigonometric graphsTransform sine, cosine and tangent graphs. Find amplitude, period, shifts, intercepts and asymptotes; interpret unknown parameters and periodic models.
Useful foundations
Review coordinate geometry for lengths and areas, quadratics for unknown side lengths or graph transformations for input and output changes.