(a) Copy and complete the following table of values for \(y = 3\sin 2\theta - \cos \theta\).
\(\theta\)
0°
30°
60°
90°
120°
150°
180°
y
-1.0
0
1.0
(b) Using a scale of 2cm to 30° 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 \(0° \leq \theta \leq 180°\). (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.
Explanation
(a)
\(\theta\)
0°
30°
60°
90°
120°
150°
180°
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 = \(9.30°, 80°, 174°\) (ii) Maximum value of y = 2.098 \(\approxeq\) 2.1 (to 1 decimal place)
