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1.7 Trigonometry

1.7 Trigonometry

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Question 135

The angular deflection θ\thetaθ of a precision tracking gimbal is governed by the equilibrium condition

4sin⁡θcos⁡θ2sin⁡θ+3=tan⁡θ,sin⁡θ≠−32 \frac{4 \sin \theta \cos \theta}{2 \sin \theta + 3} = \tan \theta, \quad \sin \theta \neq -\frac{3}{2} 2sinθ+34sinθcosθ​=tanθ,sinθ=−23​
a.

Show that this equation can be written in the form

4sin⁡3θ+2sin⁡2θ−sin⁡θ=0 4\sin^3\theta + 2\sin^2\theta - \sin\theta = 0 4sin3θ+2sin2θ−sinθ=0
[5]
b.

Determine the possible values for the angular deflection xxx of the gimbal in the range −π2<x<π2-\frac{\pi}{2} < x < \frac{\pi}{2}−2π​<x<2π​, giving your answers to 3 decimal places where appropriate.

[5]
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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