A circular window in a design studio is represented by the equation x2+y2−20x+16y+4=0x^2 + y^2 - 20x + 16y + 4 = 0x2+y2−20x+16y+4=0 in a coordinate system where units are in decimetres.
A decorative structural beam forms a chord PQ PQ\,PQ across the window. The angle subtended by the chord PQ PQ\,PQ at the centre of the window is 1.4 radians.
Calculate the area of the minor segment created between the beam PQ PQ\,PQ and the arc of the window. Give your answer to three significant figures.
317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.