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This topic solves more demanding trigonometric equations — those needing identities, double angle or addition formulae, quadratic forms in sin or cos, or the R-form — over a given interval, finding all solutions. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
Rewrite the equation using identities until it involves a single trig function, then solve as a linear or quadratic equation. Take care with the interval — a doubled angle needs a doubled range before you solve, then halve the solutions.
Before you start
Before starting, revisit identities, double angle and R form. This sits in Pure 3. The same ideas return in modelling and calculus questions.
What you learn
There is nothing new in this course — you already own every tool. Before writing anything, read the equation and ask what it is made of. An equation may contain a reciprocal function and a double angle — and the route is to deal with them in the right order. Most lost marks in this topic are not wrong answers — they are missing ones. The course works through diagnosis: choosing the tool, double angles with sec, cosec and cot, when reciprocals become double angles, finding every solution and everything combined. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
We teach Further Trig Equations as one of the Trigonometry topics in our A-level course library, at the AS year. You work through 5 concepts and 5 worked examples, testing yourself at 5 points. It sits alongside Inverse Trig Functions, R sin(θ + α) Form, Radians, Arcs & Sectors and Reciprocal Trig Functions in the same strand. Endless extra practice on this strand is available on the Trigonometry revision engine, which generates a fresh question each time.
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