Skip to content

Course home

Sign up

Trigonometry and Modelling

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051
Question 3
f(θ)=2cos⁡θ+sin⁡θ f(\theta) = 2 \cos \theta + \sin \theta f(θ)=2cosθ+sinθ

Given that f(θ)=Rcos⁡(θ−α)f(\theta) = R \cos (\theta - \alpha)f(θ)=Rcos(θ−α), where R>0 R > 0\,R>0 and 0≤α≤π2\displaystyle 0 \leq \alpha \leq \frac{\pi}{2}0≤α≤2π​

a.

Find the value of R R\,R and the value of α \alpha\,α to 3 decimal places

[4]
b.

Hence, solve for 0≤θ≤2π0 \leq \theta \leq 2\pi0≤θ≤2π, the equation

2cos⁡θ+sin⁡θ=−2 2 \cos \theta + \sin \theta = -2 2cosθ+sinθ=−2

giving your answers to 3 significant figures

[3]
c.

Calculate the minimum value of

2cos⁡4x+sin⁡4x+10 2 \cos 4x + \sin 4x + 10 2cos4x+sin4x+10
[2]
d.

Find the smallest positive value of x x\,x for which this minimum occurs, giving your answer to 3 significant figures

[3]
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.

Question bank