The temperature, θ\thetaθ °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>0 R > 0\,R>0 and 0°<α<90°0° < \alpha < 90°0°<α<90°. Give R R\,R to three significant figures and α \alpha\,α to two decimal places.
Deduce the maximum temperature inside the warehouse during the day.
Find the time of day at which this maximum temperature occurs, giving your answer to the nearest minute.
225 exam-style questions on WJEC A Level Maths 3.5 Trigonometry (A-level only), covering 3.5.1 Trigonometry (A-level only), 3.5.2 Trigonometry (A-level only), 3.5.3 Trigonometry (A-level only), 3.5.4 Trigonometry (A-level only), 3.5.5 Trigonometry (A-level only), 3.5.6 Trigonometry (A-level only), 3.5.7 Trigonometry (A-level only), and 3.5.8 Trigonometry (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.