(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 + 2cos 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 – 2cos 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.