A graphic designer is creating a logo that includes a 'shard' element. This shard is defined as the segment of a circle with centre C C\,C and radius 43 cm4\sqrt{3}\text{ cm}43 cm. The segment is bounded by the chord PQ PQ\,PQ and the arc PQPQPQ, where the angle subtended at the centre, ∠PCQ\angle PCQ∠PCQ, is π3\displaystyle \frac{\pi}{3}3π radians.
Show that the area of the shard is
k(2π−33) cm2 k(2\pi - 3\sqrt{3})\text{ cm}^2 k(2π−33) cm2where k k\,k is an integer to be found.
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.
