(a) Copy and complete the table of values for \(y = \sin x + 2 \cos x\), correct to one decimal place.
x
0°
30°
60°
90°
120°
150°
180°
210°
240°
y
2.2
-1.2
-2.0
-1.9
(b) Using a scale of 2 cm to 30° on the x- axis and 2 cm to 0.5 units on the y- axis, draw the graph of \(y = \sin x + 2\cos x\) for \(0° \leq x \leq 240°\). (c) Use your graph to solve the equation : (i) \(\sin x + 2 \cos x = 0\) ; (ii) \(\sin x = 2.1 - 2\cos x\). (d) From the graph, find y when x = 171°.
Explanation
(a)
x
0°
30°
60°
90°
120°
150°
180°
210°
240°
y
2.0
2.2
1.9
1.0
-0.1
-1.2
-2.0
-2.2
-1.9
(b) (c) (i) x = 117° ; (ii) x = 9° , 45°. (d) When x = 171°, y = -1.75.
