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1.5 Trigonometry

1.5 Trigonometry

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Question 103

A design for a decorative stained-glass window panel is shown below. The design consists of a sector OBC OBC\,OBC of a circle with centre OOO, flanked by two congruent triangles OAB OAB\,OAB and ODCODCODC. The point O O\,O lies on the straight base ADADAD. The points B B\,B and C C\,C lie on the arc of the circle. The side lengths AB AB\,AB and DC DC\,DC are equal, and the angles ∠AOB \angle AOB\,∠AOB and ∠DOC \angle DOC\,∠DOC are equal and acute.

Given that:

  • angle BOC=1.8BOC = 1.8BOC=1.8 radians
  • area of sector OBC=24.3 cm2OBC = 24.3 \text{ cm}^2OBC=24.3 cm2
  • AOD AOD\,AOD is a straight line of length 15.0 cm

Diagram of a stained-glass panel formed by sector OBC between two congruent triangles OAB and ODC, with straight base AD.

a.

Find the radius of the sector, giving your answer in cm\text{cm}cm to 2 decimal places.

[2]
b.

Find the size of angle AOBAOBAOB, in radians, to 2 decimal places.

[2]
c.

Hence find: the total area of the window panel, giving your answer in cm2\text{cm}^2cm2 to one decimal place.

[3]
d.

the total perimeter of the panel, giving your answer in cm\text{cm}cm to one decimal place.

[3]
Markscheme

1.5 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.5 Trigonometry

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.

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