A-level maths / Pure 1 / Trigonometric identities and equations
Trigonometric identities and equations
Understand the signs, connect the ratios and find every angle that works.
Choose a skill below. The models move when you choose, the working stays visible, and each lesson has practice with hints and full solutions.
- Unit circle and exact trig valuesUnderstand sine, cosine and tangent for any angle. Use quadrants, reference angles and exact values, with a unit-circle model and worked practice.
- Trigonometric identitiesUse sin²θ + cos²θ = 1 and tanθ = sinθ/cosθ to simplify, prove identities, find exact ratios and eliminate an angle while keeping domain restrictions.
- Solving trigonometric equationsSolve sine, cosine and tangent equations in a given interval. Find all solutions, understand inverse-calculator ranges and check endpoint and domain restrictions.
- Multiple-angle and shifted-angle equationsSolve equations such as sin(2x − 30°) = 1/2 by mapping the whole interval. Handle shifts, negative multipliers and unknown frequencies without losing solutions.
- Quadratic trigonometric equationsSolve quadratics in sin, cos and tan, use identities, keep zero factors and reject impossible or extraneous solutions. Includes transformed angles and biquadratic extensions.
Useful foundations
Review sine, cosine and tangent graphs for their shapes and periods, or solving quadratics for the algebra behind the final lesson.