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.
278 exam-style questions on Edexcel A Level Maths Radians, covering 5.1 Radian Measure, 5.2 Arc Length, 5.3 Areas of Sectors and Segments, 5.4 Solving Trigonometric Equations, and 5.5 Small Angle Approximations. Each one has a worked solution and a mark scheme showing where the marks go.