At GCSE
At GCSE Higher you use SOHCAHTOA on right-angled triangles, apply the sine and cosine rules to any triangle, find the area with ½ab sin C, and learn the exact values for 30°, 45° and 60°.
GCSEA-LevelAQAEdexcelOCR
Trigonometry revision — GCSE & A-Level Maths
Trigonometry appears in every UK Maths exam from GCSE Higher upwards. You must use SOHCAHTOA on right-angled triangles, the sine and cosine rules on any triangle, and know the exact values for 30°, 45° and 60°.
At A-Level the topic expands into radians, identities (sin²θ + cos²θ = 1), solving equations on a given interval and graph transformations. Calculators in degree or radian mode — make sure you check before each question.
At A-Level
At A-Level you work in radians (arc length s = rθ, sector area = ½r²θ), use identities (sin²θ + cos²θ = 1, tan = sin/cos), solve trig equations on a given interval, and apply transformations to the graphs of sin, cos and tan.
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Example flashcards
Q: State SOHCAHTOA.
A: sin = opp/hyp, cos = adj/hyp, tan = opp/adj — for a right-angled triangle.
Q: Write the cosine rule.
A: a² = b² + c² − 2bc·cos A.
Q: What is sin 30° as an exact value?
A: ½.
Q: Give the trig identity linking sin and cos.
A: sin²θ + cos²θ = 1.
Quick summary
Trigonometry is a high-yield Maths topic for GCSE and A-Level students (AQA, Edexcel, OCR). At A-Level you work in radians (arc length s = rθ, sector area = ½r²θ), use identities (sin²θ + cos²θ = 1, tan = sin/cos), solve trig equations on a given interval, and apply transformations to the graphs of sin, cos and tan. Examiners reward precise definitions and applied explanations — focus on the core ideas and the small set of terms that come up every series.
Key terms
- Sine
- Cosine
- Tangent
- SOHCAHTOA
- Sine rule
- Cosine rule
- Radian
- Identity
- Amplitude
Trigonometry FAQs
How do I know whether to use the sine or cosine rule?+
Use sine rule when you know a side and its opposite angle. Use cosine rule when you have three sides, or two sides and the angle between them.
How do I convert between degrees and radians?+
Multiply by π/180 to go from degrees to radians; multiply by 180/π to go the other way. So 90° = π/2 rad.
Why does the sine rule sometimes give two answers (the ambiguous case)?+
Because sin θ = sin(180° − θ), so for a given opposite ratio there may be both an acute and an obtuse solution. Check whether both fit the triangle.
What is the period of y = sin(2x)?+
180° (or π radians) — the horizontal stretch factor of 1/2 halves the period.
Related Maths topics
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