Pure Maths
A-Level Trigonometry
Trigonometry moves from right-angled triangles to identities, radians and equations with multiple solutions across a given interval.
What you need to know
- Exact values for 0, 30, 45, 60 and 90 degrees
- Radian measure, arc length and sector area
- The identities sin²θ + cos²θ = 1 and tanθ = sinθ/cosθ
- Solving trigonometric equations over an interval
Key concepts
- Sketching the graph is the fastest way to find every solution in range.
- Arc length s = rθ and sector area = ½r²θ both require radians.
- Double angle formulae let you reduce an equation to a single angle.
Common mistakes
- Giving only the principal value instead of all solutions in the interval
- Leaving the calculator in degrees when the question uses radians
- Dividing by cosθ and losing solutions where cosθ = 0
Example question
What is the exact value of ?
Show explanation
From the 30-60-90 triangle, sin 30° = 1/2.
Practise Trigonometry
4 original questions with worked explanations, mixed across easy, medium and challenging difficulty.
Trigonometry questions students ask
- Should I work in degrees or radians?
- Follow the question. If the interval is written with π, work in radians throughout.