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3.5 Trigonometry (A-level only)

3.5 Trigonometry (A-level only)

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Question 86

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

3.5 Trigonometry (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.5 Trigonometry (A-level only)

225 exam-style questions on WJEC A Level Maths 3.5 Trigonometry (A-level only), covering 3.5.1 Trigonometry (A-level only), 3.5.2 Trigonometry (A-level only), 3.5.3 Trigonometry (A-level only), 3.5.4 Trigonometry (A-level only), 3.5.5 Trigonometry (A-level only), 3.5.6 Trigonometry (A-level only), 3.5.7 Trigonometry (A-level only), and 3.5.8 Trigonometry (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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