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1.5 Trigonometry

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Question 62

A designer is creating a custom metal plate in the shape of a logo, PQRSPPQRS PPQRSP. The logo consists of a major sector PQROPQROPQRO of a circle with centre OOO and radius 12 cm12\text{ cm}12 cm, joined to a triangle POSPOSPOS. The point SSS lies on the radius OROROR. The length of the straight edge PSPSPS is 10 cm10\text{ cm}10 cm and the angle POSPOSPOS is 0.75 radians0.75\text{ radians}0.75 radians.

a.

Find the area of the major sector PQROPQROPQRO, giving your answer to one decimal place.

[2]
b.

Given that the angle PSOPSOPSO is obtuse,

find the size of angle PSOPSOPSO in radians, giving your answer to 3 decimal places.

[3]
c.

Determine the total perimeter of the shape PQRSPPQRS PPQRSP, giving your answer 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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