Edexcel Mathematics October 2021 · Paper 2 · Question 15 · ExamRizz

ExamRizzEdexcel MathematicsMathematics

October 2021 · Paper 2 · Question 15 · 11 marks

15. (a) Express 2cos θ – sin θ in the form R cos ( θ + α), where R > 0 and 0 < α < π 2 Give the exact value of R and the value of α in radians to 3 decimal places. (3) Water levelH metresP C Figure 6 Figure 6 shows the cross-section of a water wheel. The wheel is free to rotate about a fixed axis through the point C. The point P is at the end of one of the paddles of the wheel, as shown in Figure 6. The water level is assumed to be horizontal and of constant height. The vertical height, H metres, of P above the water level is modelled by the equation H = 3 + 4 cos (0.5t ) – 2 sin (0.5 t) where t is the time in seconds after the wheel starts rotating. Using the model, find (b) (i) the maximum height of P above the water level, (ii) the value of t when this maximum height first occurs, giving your answer to one decimal place. (3) In a single revolution of the wheel, P is below the water level for a total of T seconds. According to the model, (c) find the value of T giving your answer to 3 significant figures. (Solutions based entirely on calculator technology are not acceptable .) (4) In reality, the water level may not be of constant height. (d) Explain how the equation of the model should be refined to take this into account. (1) 45 46 47 48  

Lesson: Definitions of Sine, Cosine and Tangent and Exact Values