The temperature, θ∘C\theta^\circ\text{C}θ∘C, inside a warehouse is modelled by the equation
θ=8+2sin(15t−160)+3cos(15t−160) \theta = 8 + 2 \sin(15t - 160) + 3 \cos(15t - 160) θ=8+2sin(15t−160)+3cos(15t−160)where t t\,t is the number of hours after midnight.
Express 2sinx+3cosx2 \sin x + 3 \cos x2sinx+3cosx 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∘
Deduce the maximum temperature of the room during this day,
Find the time of day when the maximum temperature occurs, giving your answer to the nearest minute
137 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.