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Trigonometry and Modelling

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Question 173
f(x)=Rcos⁡(x+α) f(x) = R \cos (x + \alpha) f(x)=Rcos(x+α)

Given that R=5R = 5R=5 and α=tan⁡−1(43)\displaystyle \alpha = \tan^{-1}\left(\frac{4}{3}\right)α=tan−1(34​), where R>0 R > 0\,R>0 and 0≤α≤900 \leq \alpha \leq 900≤α≤90,

a.

Show that f(x)=3cos⁡x−4sin⁡xf(x) = 3 \cos x - 4 \sin xf(x)=3cosx−4sinx

[4]
b.

Hence solve, for 0≤x≤3600 \leq x \leq 3600≤x≤360, the equation

3cos⁡x−4sin⁡x=1 3 \cos x - 4 \sin x = 1 3cosx−4sinx=1

Give your answers to 1 decimal place.

[5]
c.

Write down the minimum value of 3cos⁡x−4sin⁡x3 \cos x - 4 \sin x3cosx−4sinx

[1]
d.

Find, to 1 decimal place, the smallest positive value of x x\,x for which this minimum occurs

[2]
Markscheme

Trigonometry and Modelling Questions

  1. A Level
  2. /Maths
  3. /Trigonometry and Modelling

348 exam-style questions on Edexcel A Level Maths Trigonometry and Modelling, covering 7.1 Addition Formulae, 7.2 Double Angle Formulae, 7.3 Solving Trigonometric Equations, 7.4 Simplifying a cos x +- b sin x, 7.5 Proving Trigonometric Identities, and 7.6 Modelling with Trigonometric Functions. Each one has a worked solution and a mark scheme showing where the marks go.

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