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1.7 Trigonometry

1.7 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

1.7 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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