Non-right-triangle and Exact Trigonometry
Use sine and cosine rules, trigonometric area, exact values and 2D or 3D modelling.
How to study for GCSE Mathematics
Use 601 original multiple-choice questions to learn connected methods, explain why they work, practise exact non-calculator execution and use a calculator strategically on designated papers.
Core concepts
Concept 1
Sine rule
Exam cue: Match opposite side-angle pairs for the sine rule; use the cosine rule for SAS or SSS; preserve exact values until the required rounding.
Concept 2
Cosine rule and triangle area
Exam cue: Use triangle angle and side-size relationships, including the ambiguous sine case where relevant.
Concept 3
Exact trigonometric values
Exam cue: Represent the information clearly, choose a justified method and communicate each step with correct notation and units.
Targeted study blocks
Tier coverage
Foundation core with Higher-tier extensions
The sine rule, cosine rule, trigonometric area formula, exact trigonometric values and extended 3D modelling are Higher-only common-core techniques.
Calculator structure
Prepare for calculator and non-calculator papers
Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Risk pitfalls and guardrails
Pairing a side with a non-opposite angle in the sine rule.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Giving an unsupported answer when the command requires working, proof, reasoning or interpretation.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Assuming a topic belongs only to calculator or non-calculator papers; any specification content can be assessed on any paper.
Guardrail: Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Memory anchors
Sine rule pairing
Each side is paired with its opposite angle.
Cosine rule use
Use for SAS to find a side or SSS to find an angle.
Triangle area with trig
Area = 1/2 ab sin C for the included angle C.
Non-right-triangle and Exact Trigonometry: method
Match opposite side-angle pairs for the sine rule; use the cosine rule for SAS or SSS; preserve exact values until the required rounding.
Non-right-triangle and Exact Trigonometry: check
Use triangle angle and side-size relationships, including the ambiguous sine case where relevant.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Higher · AO1 technique · Non-calculator — What is the exact value of sin 30°?
Higher · AO1 technique · Non-calculator — What is the exact value of cos 45°?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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