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1.7 Trigonometry

1.7 Trigonometry

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Question 157

A mechanical component for a precision pendulum clock is designed using a triangular metal plate OAB OAB\,OAB attached to a weighted circular sector OBC OBC\,OBC with centre OOO.

In this design:

  • OB=6.5 cmOB = 6.5\text{ cm}OB=6.5 cm
  • AB=3.5 cmAB = 3.5\text{ cm}AB=3.5 cm
  • angle AOB=π12\displaystyle AOB = \frac{\pi}{12}AOB=12π​ radians
  • angle OAB OAB\,OAB is an obtuse angle
a.

Determine the size of angle OABOABOAB, giving your answer in radians to 4 significant figures.

[3]
b.

Calculate the area of the triangular plate OAB OAB\,OAB in cm2\text{cm}^2cm2, giving your answer to 3 significant figures.

[2]
c.

Given that the ratio of the area of the weighted sector OBC OBC\,OBC to the area of the triangular plate OAB OAB\,OAB is 7:4 7:4\,7:4

Show that angle BOC BOC\,BOC is 0.224 radians to 3 significant figures.

[3]
d.

Hence find the total perimeter of the component, in cm, to the nearest integer.

[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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