(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) \(\sin 2x - \cos x = 0 \implies x = 30°, 90°, 150°\).
