(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°.
