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1.5 Trigonometry

1.5 Trigonometry

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Question 124

A designer is drafting a logo for a renewable energy company. The design features a central polished circular sector OBCOBCOBC, with centre OOO, flanked by two identical triangular 'rays', OABOABOAB and ODCODCODC. The points A,O,A, O,A,O, and DDD lie on a straight horizontal line. The vertices BBB and CCC lie on the circular arc that forms the boundary of the sector.

Given that:

  • angle BOC=1.8BOC = 1.8BOC=1.8 radians
  • the area of sector OBC=25 cm2OBC = 25 \text{ cm}^2OBC=25 cm2
  • AODAODAOD is a straight line segment with a total length of 10.0 cm10.0 \text{ cm}10.0 cm
a.

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

[3]
b.

Calculate the size of angle AOBAOBAOB in radians, giving your answer to 2 decimal places.

[2]
c.

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

[3]
d.

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

[4]
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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