(a) Copy and complete the table of values for \(y = \sin x + 2 \cos x\), correct to one decimal place.
x
0^\circ
30^\circ
60^\circ
90^\circ
120^\circ
150^\circ
180^\circ
210^\circ
240^\circ
y
2.2
-1.2
-2.0
-1.9
(b) Using a scale of 2 cm to 30^\circ 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 \(0^\circ \leq x \leq 240^\circ\).
(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^\circ.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
x
0^\circ
30^\circ
60^\circ
90^\circ
120^\circ
150^\circ
180^\circ
210^\circ
240^\circ
y
2.0
2.2
1.9
1.0
-0.1
-1.2
-2.0
-2.2
-1.9
(b)
(c) (i) x = 117^\circ ; (ii) x = 9^\circ , 45^\circ.
(d) When x = 171^\circ, y = -1.75.
Source: Myschool Past Questions Archive (Record #52924)