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1.7 Trigonometry

1.7 Trigonometry

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Question 117

A designer is drafting a logo for a renewable energy company. The design features a central polished circular sector OBCOBCOBC, with centre OOO, flanked by two identical triangular 'rays', OABOABOAB and ODCODCODC. The points A,O,A, O,A,O, and DDD lie on a straight horizontal line. The vertices BBB and CCC lie on the circular arc that forms the boundary of the sector.

Given that:

  • angle BOC=1.8BOC = 1.8BOC=1.8 radians
  • the area of sector OBC=25 cm2OBC = 25 \text{ cm}^2OBC=25 cm2
  • AODAODAOD is a straight line segment with a total length of 10.0 cm10.0 \text{ cm}10.0 cm
a.

Determine the radius of the circular sector, giving your answer in cm\text{cm}cm to 2 decimal places.

[3]
b.

Calculate the size of angle AOBAOBAOB in radians, giving your answer to 2 decimal places.

[2]
c.

Hence find: the total area of the logo, giving your answer in cm2\text{cm}^2cm2 to one decimal place.

[3]
d.

the total perimeter of the logo, giving your answer in cm\text{cm}cm 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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