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1.8 E: Trigonometry

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Question 99

The diagram shows the design for a decorative glass panel in the shape of a semicircle with center O O\,O and diameter AOEAOEAOE. The points B B\,B and D D\,D lie on the arc of the semicircle such that the chord BD BD\,BD is parallel to the diameter AEAEAE. A specific section of the glass, a segment labeled RRR, is bounded by the chord BD BD\,BD and the arc BCDBCDBCD. The radius of the semicircle is 8 cm and the angle DOE DOE\,DOE is 0.45 radians.

Semicircular glass panel with diameter AOE, horizontal chord BD, centre O, angle DOE of 0.45 radians, radius 8 cm, and shaded segment R bounded by chord BD and arc BCD.

a.

Show that, to 3 decimal places, the angle BOD BOD\,BOD is 2.242 radians.

[3]
b.

Find the area of the shaded glass segment RRR, giving your answer in cm2\text{cm}^2cm2 to one decimal place.

[3]
c.

Find the perimeter of the shaded region RRR, giving your answer in cm\text{cm}cm to one decimal place.

[4]
Markscheme

1.8 E: Trigonometry Questions

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

317 exam-style questions on AQA A Level Maths 1.8 E: Trigonometry, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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