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1.8 E: Trigonometry

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Question 122

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]

1.8 E: Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.8 E: Trigonometry

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.

Question bank