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∘, and hence 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
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.