(a) Copy and complete the following table of values for \(y = 9 \cos x + 5 \sin x\) to one decimal place.
| x | 0° | 30° | 60° | 90° | 120° | 150° | 180° | 210° |
| y | 10.3 | -0.2 | -5.3 | -10.3 |
(b) Using a scale of 2cm to 30° on the x- axis and 2 cm to 1 unit on the y- axis, draw the graph of \(y = 9 \cos x + 5 \sin x\) for \(0° \leq x \leq 210°\).
(c) Use your graph to solve the equation: (i) \(9\cos x + 5\sin x = 0\); (ii) \(9\cos x+ 5\sin x = 3.5\), correct to the nearest degree.
(d) Find the maximum value of y correct to one decimal place.
Explanation
| x | 0° | 30° | 60° | 90° | 120° | 150° | 180° | 210° |
| y | 9 | 10.3 | 8.8 | 5 | -0.2 | -5.3 | -9 | -10.3 |
(b) 
(c)(i) From the graph, \(9\cos x + 5\sin x = 0 \implies x = 119°\)
(d) Maximum value of y = 10.3.