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1.7 Trigonometry

1.7 Trigonometry

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Question 94

An aerospace engineer is designing a solar-collecting aperture for a satellite in the shape of a sector of a circle. A specialized gold-plated conductive gasket must be fitted along the entire perimeter of the aperture to prevent electromagnetic interference. The gasket costs £14.40 £14.40\,£14.40 per metre. One prototype design has a radius of 15 m and a central angle of 0.6 radians.

a.

(i) Determine the area of the solar-collecting surface of this prototype aperture.

[2]
b.

(ii) Calculate the total cost of the gasket required for this prototype.

[2]
c.

For a different mission, the aperture must be redesigned to have a fixed surface area of 45 m2.

(i) Show that the cost, £C£C£C, of the gasket for this redesigned aperture is given by

C=28.8(45r+r) C = 28.8\left(\frac{45}{r} + r\right) C=28.8(r45​+r)

where r r\,r is the radius measured in metres.

[3]
d.

(ii) Hence, find the value of r r\,r for which the gasket cost is minimized, and justify that your value gives a minimum cost.

[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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