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1.7 Trigonometry

1.7 Trigonometry

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Question 136

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

1.7 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.7 Trigonometry

317 exam-style questions on OCR (MEI) A Level Maths 1.7 Trigonometry, covering 1.7.1 Solve right-angled triangles, 1.7.2 Definitions of sin, cos and tan for any angle, 1.7.3 Graphs of sin, cos and tan, 1.7.4 Exact values of trig functions (degrees), 1.7.5 Area of a triangle, 1.7.6 Sine and cosine rules, 1.7.7 Identity tan = sin/cos, 1.7.8 Identity sin^2 + cos^2 = 1, 1.7.9 Solve simple trigonometric equations, 1.7.10 Exact values of trig functions (radians) (A-level only), 1.7.11 Inverse trigonometric functions (A-level only), 1.7.12 Radians and degree conversion (A-level only), 1.7.13 Arc length and area of a sector (A-level only), 1.7.14 Small angle approximations (A-level only), 1.7.15 Sec, cosec and cot functions (A-level only), 1.7.16 Graphs of reciprocal trig functions (A-level only), 1.7.17 Pythagorean identities for sec and cosec (A-level only), 1.7.18 Compound angle formulae (A-level only), 1.7.19 Double angle identities (A-level only), 1.7.20 Expressions for a cos θ ± b sin θ (A-level only), 1.7.21 Use identities to solve equations (A-level only), 1.7.22 Proofs involving trigonometric functions (A-level only), 1.7.23 Trig to solve problems in context (A-level only), and 1.7 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.

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