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Trigonometry and Modelling

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Question 70

The temperature, θ∘C\theta^\circ\text{C}θ∘C, inside a warehouse is modelled by the equation

θ=8+2sin⁡(15t−150)+2cos⁡(15t−150) \theta = 8 + 2 \sin(15t - 150) + 2 \cos(15t - 150) θ=8+2sin(15t−150)+2cos(15t−150)

where t t\,t is the number of hours after midnight.

a.

Express 2sin⁡x+2cos⁡x2 \sin x + 2 \cos x2sinx+2cosx in the form Rsin⁡(x+α)R \sin(x + \alpha)Rsin(x+α), where R R\,R and α \alpha\,α are constants, R>0 R > 0\,R>0 and 0<α<90∘0 < \alpha < 90^\circ0<α<90∘

[3]
b.

Deduce the maximum temperature of the room during this day,

[1]
c.

Find the time of day when the maximum temperature occurs, giving your answer to the nearest minute

[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.

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