(a) Copy and complete the table of values for \(y = \sin x + 2 \cos x\), correct to one decimal place.
| x | 0° | 30° | 60° | 90° | 120° | 150° | 180° | 210° |
240° |
| y | 2.2 | -1.2 | -2.0 | -1.9 |
(b) Using a scale of 2 cm to 30° on the x- axis and 2 cm to 0.5 units on the y- axis, draw the graph of \(y = \sin x + 2\cos x\) for \(0° \leq x \leq 240°\).
(c) Use your graph to solve the equation : (i) \(\sin x + 2 \cos x = 0\) ; (ii) \(\sin x = 2.1 – 2\cos x\).
(d) From the graph, find y when x = 171°.
Explanation
(a)
| x | 0° | 30° | 60° | 90° | 120° | 150° | 180° | 210° | 240° |
| y | 2.0 | 2.2 | 1.9 | 1.0 | -0.1 | -1.2 | -2.0 | -2.2 | -1.9 |
(b) 
(c) (i) x = 117° ; (ii) x = 9° , 45°.
(d) When x = 171°, y = -1.75.