(a) Copy and complete the table of the relation \(y = 2\sin x – \cos 2x\).
| x | 0° | 30° | 60° | 90° | 120° | 150° | 180° |
| y | 0.5 | -1.0 |
Using a scale of 2 cm to 30° on the x- axis and 2 cm to 0.5 unit on the y- axis, draw the graph of \(y = 2\sin x – \cos 2x\), for \(0° \leq x \leq 180°\).
(b) Using the same axes, draw the graph of \(y = 1.25\).
(c) Use your graphs to find the : (i) values of x for which \(2\sin x – \cos 2x = 0\) ; (ii) the roots of the equation \(2\sin x – \cos 2x = 1.25\).
Explanation
(a) \(y = 2\sin x - \cos 2x\)
| x | 0° | 30° | 60° | 90° | 120° | 150° | 180° |
| y | -1.0 | 0.5 | 2.2 | 3.0 | 2.2 | 0.5 | -1.0 |
(b) 