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1.5 Trigonometry

1.5 Trigonometry

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Question 53

A designer is creating a specialized acoustic panel. The panel ABCDA ABCDA\,ABCDA consists of a major sector ACBA ACBA\,ACBA of a circle with centre C C\,C and radius 10 cm, and a triangular region ACDACDACD, as shown in the geometry below. The point D D\,D lies on the radius CBCBCB. The radius of the circle is 10 cm, the length of AD AD\,AD is 9 cm and the angle ACD ACD\,ACD is 0.8 radians0.8\text{ radians}0.8 radians.

Diagram of panel ABCDA formed from a major sector with centre C and triangle ACD, where D lies on radius CB, AC is 10 cm, AD is 9 cm and angle ACD is 0.8 radians.

a.

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

[3]
b.

Given that the angle ADC ADC\,ADC is obtuse,

find the size of angle ADCADCADC, giving your answer to 3 decimal places.

[3]
c.

Hence find the perimeter of the panel ABCDAABCDAABCDA, 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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