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1.7 Trigonometry

1.7 Trigonometry

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Question 193

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:

  • The central angle ∠POQ \angle POQ\,∠POQ of the minor sector is 0.8 radians.
  • The length of the outer arc PQ PQ\,PQ is 20 m.
  • The ratio of the lengths PR:RO=1:4PR : RO = 1 : 4PR:RO=1:4.
a.

Show that RO=20 mRO = 20\text{ m}RO=20 m.

[4]
b.

Calculate the total perimeter of the amphitheatre stage, giving your answer in m to 3 significant figures.

[5]
c.

Calculate the total surface area of the stage, giving your answer in m2\text{m}^2m2 to the nearest integer.

[5]
Markscheme

1.7 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.7 Trigonometry

317 exam-style questions on OCR (MEI) A Level Maths 1.7 Trigonometry, covering 1.7.1 Solve right-angled triangles, 1.7.2 Definitions of sin, cos and tan for any angle, 1.7.3 Graphs of sin, cos and tan, 1.7.4 Exact values of trig functions (degrees), 1.7.5 Area of a triangle, 1.7.6 Sine and cosine rules, 1.7.7 Identity tan = sin/cos, 1.7.8 Identity sin^2 + cos^2 = 1, 1.7.9 Solve simple trigonometric equations, 1.7.10 Exact values of trig functions (radians) (A-level only), 1.7.11 Inverse trigonometric functions (A-level only), 1.7.12 Radians and degree conversion (A-level only), 1.7.13 Arc length and area of a sector (A-level only), 1.7.14 Small angle approximations (A-level only), 1.7.15 Sec, cosec and cot functions (A-level only), 1.7.16 Graphs of reciprocal trig functions (A-level only), 1.7.17 Pythagorean identities for sec and cosec (A-level only), 1.7.18 Compound angle formulae (A-level only), 1.7.19 Double angle identities (A-level only), 1.7.20 Expressions for a cos θ ± b sin θ (A-level only), 1.7.21 Use identities to solve equations (A-level only), 1.7.22 Proofs involving trigonometric functions (A-level only), 1.7.23 Trig to solve problems in context (A-level only), and 1.7 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.

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