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1.7 Trigonometry

1.7 Trigonometry

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Question 77

An automated tracking sensor for a wind turbine calculates its optimal inclination angle θ\thetaθ relative to the wind direction. For a specific range of wind speeds, the mechanical equilibrium of the sensor is maintained when

a.

Show that the equation

6tan⁡θ=cos⁡θ 6 \tan \theta = \cos \theta 6tanθ=cosθ

may be rewritten in the form

sin⁡2θ+6sin⁡θ−1=0 \sin^2 \theta + 6 \sin \theta - 1 = 0 sin2θ+6sinθ−1=0
[3]
b.

Hence solve, for 0∘≤x≤180∘0^\circ \le x \le 180^\circ0∘≤x≤180∘, the equation

6tan⁡(2x+10∘)=cos⁡(2x+10∘) 6 \tan (2x + 10^\circ) = \cos (2x + 10^\circ) 6tan(2x+10∘)=cos(2x+10∘)

giving your answers to 2 decimal places.

[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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