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1 Unit 1: Pure Mathematics A

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Question 184

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]
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1 Unit 1: Pure Mathematics A Questions

  1. A Level
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