(a) Copy and complete the following table of values for \(y = 3\sin 2\theta - \cos \theta\).
\(\theta\)
0^\circ
30^\circ
60^\circ
90^\circ
120^\circ
150^\circ
180^\circ
y
-1.0
0
1.0
(b) Using a scale of 2cm to 30^\circ on the \(\theta\) axis and 2cm to 1 unit on the y- axis, draw the graph of \(y = 3 \sin 2\theta - \cos \theta\) for \(0^\circ \leq \theta \leq 180^\circ\).
(c) Use your graph to find the : (i) solution of the equation \(3 \sin 2\theta - \cos \theta = 0\), correct to the nearest degree; (ii) maximum value of y, correct to one decimal place.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
\(\theta\)
0^\circ
30^\circ
60^\circ
90^\circ
120^\circ
150^\circ
180^\circ
y
-1.0
1.732
2.098
0
-2.098
-1.732
1.0
(b)
(c)(i) Solution of \(3 \sin 2 \theta - \cos \theta = 0\) is at y = 0
= \(9.30^\circ, 80^\circ, 174^\circ\)
(ii) Maximum value of y = 2.098 \(\approxeq\) 2.1 (to 1 decimal place)
Source: Myschool Past Questions Archive (Record #54575)