(a) Copy and complete the table of values for \(y = 1 – 4\cos x\).
| x | 0° | 30° | 60° | 90° | 120° | 150° | 180° | 210° | 240° | 270° |
300° |
| y | -3.0 | 1.0 | 4.5 | -1.0 |
(b) Using a scale of 2cm to 30° on the x- axis and 2cm to 1 unit on the y- axis, draw the graph of \(y = 1 – 4\cos x\) for \(0° \leq x \leq 360°\).
(c) Use the graph to : (i) solve the equation \(1 – 4\cos x = 0\) ; (ii) find the value of y when x = 105° ; (iii) find x when y = 1.5.
Explanation
(a)
| x | 0° | 30° | 60° | 90° | 120° | 150° | 180° | 210° | 240° | 270° |
300° |
| y | -3.0 | -2.5 | -1.0 | 1.0 | 3.0 | 4.5 | 5.0 | 4.5 | 3.0 | 1.0 | -1.0 |
(b) 
(c)(i) x = 75° or x = 285°
(ii) When x = 105°, y = 2.
(iii) When y = 1.5, x = 96° or x = 264°.