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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