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1.5 Trigonometry

1.5 Trigonometry

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Question 139

An architect is designing a custom semicircular stained-glass window with center CCC and a diameter PCQPCQPCQ of length 16 m16\text{ m}16 m. To reinforce the structure, a horizontal metal support beam STSTST is placed parallel to the diameter PCQPCQPCQ, such that the endpoints SSS and TTT lie on the semicircular arc. The design specifies that the angle TCQTCQTCQ is 0.450.450.45 radians. A specific segment of tinted glass, labeled WWW, is bounded by the beam STSTST and the minor arc STSTST.

a.

Show that, to 3 decimal places, the angle SCTSCTSCT is 2.2422.2422.242 radians.

[2]
b.

Calculate the area of the tinted glass segment WWW, giving your answer in m2\text{m}^2m2 to one decimal place.

[3]
c.

Determine the total perimeter of the tinted glass segment WWW, giving your answer in m\text{m}m to one decimal place.

[3]
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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