(a) Using a scale of 2 cm to 30° on the x- axis, 2 cm to 0.2 units on the y- axis, on the same graph sheet, draw the graphs of (y = sin 2x) and (y = cos x) for (0° leq x leq 210°) at intervals of 30°.
(b) Using the graphs in (a), find the truth set of :
(i) (sin 2x = 0) ; (ii) (sin 2x – cos x = 0).
Explanation
(a) Table of values for (y = sin 2x) and (y = cos x).
| x | 0° | 30° | 60° | 90° | 120° | 150° | 180° | 210° |
| (y = sin 2x) | 0 | 0.87 | 0.87 | 0 | -0.87 | -0.87 | 0 | 0.87 |
| (y = cos x) | 1 | 0.87 | 0.50 | 0 | -0.50 | -0.87 | -1 | -0.87 |
(b)(i) (sin 2x = 0 implies x = 0°, 90°, 180°)
(ii) (sin 2x – cos x = 0 implies x = 30°, 90°, 150°).