(a) Copy and complete the following table of values for \(y = 9 \cos x + 5 \sin x\) to one decimal place.
x
0^\circ
30^\circ
60^\circ
90^\circ
120^\circ
150^\circ
180^\circ
210^\circ
y
10.3
-0.2
-5.3
-10.3
(b) Using a scale of 2cm to 30^\circ on the x- axis and 2 cm to 1 unit on the y- axis, draw the graph of \(y = 9 \cos x + 5 \sin x\) for \(0^\circ \leq x \leq 210^\circ\).
(c) Use your graph to solve the equation: (i) \(9\cos x + 5\sin x = 0\); (ii) \(9\cos x+ 5\sin x = 3.5\), correct to the nearest degree.
(d) Find the maximum value of y correct to one decimal place.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
x
0^\circ
30^\circ
60^\circ
90^\circ
120^\circ
150^\circ
180^\circ
210^\circ
y
9
10.3
8.8
5
-0.2
-5.3
-9
-10.3
(b)
(c)(i) From the graph, \(9\cos x + 5\sin x = 0 \implies x = 119^\circ\)
(d) Maximum value of y = 10.3.
Source: Myschool Past Questions Archive (Record #54428)