An amphitheatre stage is designed as a composite of two circular sectors sharing a common centre OOO. The outer part of the stage is a minor sector POQ POQ\,POQ with radius OP OP\,OP and arc PQPQPQ. The inner part is a reflex (major) sector ROS ROS\,ROS with radius OR OR\,OR and arc RTSRTSRTS. It is given that points R R\,R and S S\,S lie on the radii OP OP\,OP and OQ OQ\,OQ respectively, such that O,R,P O, R, P\,O,R,P and O,S,Q O, S, Q\,O,S,Q are collinear.
The layout specifications are as follows:
Show that RO=20 mRO = 20\text{ m}RO=20 m.
Calculate the total perimeter of the amphitheatre stage, giving your answer in m to 3 significant figures.
Calculate the total surface area of the stage, giving your answer in m2\text{m}^2m2 to the nearest integer.
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.
