a. Express 7 cos 24 sin in the form R cos ( + ), with R > 0 and 0 <

a. Express 7 cos θ − 24 sin θ in the form R cos (θ + α), with R > 0 and 0 < α < 90°.

b. The graph of y = 7 cos θ − 24 sin θ meets the y-axis at P. State the coordinates of P.

c. Write down the maximum and minimum values of 7 cos θ − 24 sin θ.

d. Deduce the number of solutions, in the interval 0 < θ < 360°, of the following equations:

i. 7 cos θ − 24 sin θ = 15

ii. 7 cos θ − 24 sin θ = 26

iii. 7 cos θ − 24 sin θ = −25