Trigonometry
Use sine and cosine rules, triangle area, radians, exact values, identities, graphs and interval solutions.
How to prepare for the current TMUA
Secure the shared mathematical specification, practise application in unfamiliar settings, then make every Paper 2 implication and proof step explicit.
Core concepts
Concept 1
Select a triangle rule from the available side-angle information, including the ambiguous sine-rule case.
Exam cue: Check whether a known side is paired with its opposite angle.
Concept 2
Use radian measure for arcs, sectors and periodic functions.
Exam cue: Record degree or radian mode in the working even without a calculator.
Concept 3
Solve trigonometric equations by identity, symmetry, periodicity and interval control.
Exam cue: Find a principal solution, then generate all solutions in the stated interval.
Risk pitfalls and guardrails
Mixing degrees and radians.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Missing the second triangle in an ambiguous sine-rule case.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Returning only one periodic solution.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Memory anchors
Sine rule
Use known or required opposite side-angle pairs.
Cosine rule
Use three sides or two sides and the included angle.
Triangle area
Area = ½ab sin C for the included angle C.
Radian arc
s = rθ when θ is measured in radians.
Core identity
sin²θ + cos²θ = 1.
Interval finish
Symmetry and period must be checked against the given range.
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
In triangle ABC, a=7, b=5 and cos C=1/5. What is c²?
A triangle has sides 8 and 10 enclosing angle 30°. What is four times its area?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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