a. Express 65 cos 20 sin in the form R cos ( + ), where R > 0 and 0 <

a. Express 65 cos θ − 20 sin θ in the form R cos (θ + α), where R > 0 and 0 < α < π/2. Give the value of α correct to 4 decimal places. A city wants to build a large circular wheel as a tourist attraction. The height of a tourist on the circular wheel is modelled by the equation H = 70 − 65 cos 0.2t + 20 sin 0.2t where H is the height of the tourist above the ground in metres, t is the number of minutes after boarding and the angles are given in radians. Find: 

b. The maximum height of the wheel

c. The time for one complete revolution./2
d. The number of minutes the tourist will be over 100 m above the ground in each revolution.