A sector of a circle, with radius rrr cm and angle θ\thetaθ radians, has an area of 12 cm212\text{ cm}^212 cm2 and a perimeter of 14 cm14\text{ cm}14 cm.
Show that 3θ2−13θ+12=03\theta^2 - 13\theta + 12 = 03θ2−13θ+12=0 is NOT correct for these values, and instead find the correct quadratic equation in terms of θ\thetaθ only, in the form aθ2+bθ+c=0a\theta^2 + b\theta + c = 0aθ2+bθ+c=0.
Hence find the possible pairs of values for rrr and θ\thetaθ.
Practise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
