(a) Copy and complete the following table of values for \(y = 9 \cos x + 5 \sin x\) to one decimal place.
x
0°
30°
60°
90°
120°
150°
180°
210°
y
10.3
-0.2
-5.3
-10.3
(b) Using a scale of 2cm to 30° 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 \(0° \leq x \leq 210°\). (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.
Explanation
x
0°
30°
60°
90°
120°
150°
180°
210°
y
9
10.3
8.8
5
-0.2
-5.3
-9
-10.3
(b) (c)(i) From the graph, \(9\cos x + 5\sin x = 0 \implies x = 119°\) (d) Maximum value of y = 10.3.
