(a) Copy and complete the table of values for y = 2 cos x + 3 sin x for 0\(^o\) \(\geq\) x \(\geq\) 360\(^o\)
| x | 0\(^o\) | 60\(^0\) | 120\(^o\) | 180\(^o\) | 240\(^o\) | 300\(^o\) | 360\(^o\) |
| y | 2.0 | – 3.6 |
(b) Using a scale of 2cm to 60\(^o\) on the x-axis and 2cm to 1 unit in the y-axis, draw the graph of y = 2 cos x + 3 sin x for 0\(^o\) \(\geq\) 360\(^o\)
(c) Using the graph,
(i) Solve 2 cos x + 3 sin x = -1
(ii) Find, correct to one decimal place, the value of y when x = 342\(^o\)
Explanation
(a) When x = 60\(^o\)
y = 2cos 60\(^o\) + 3sin 60\(^o\)
y = 3.6
When x = 120\(^o\)
y = 2 cos 120\(^o\) + 3 sin 180\(^o\)
y = 1.6
When x = 180\(^o\)
y = 2 cos 180\(^o\) + 3 sin 180\(^o\)
y = 2
When x = 300\(^o\)
y = 2 cos 300\(^o\) + 3 sin 300\(^o\)
y = 1.6
when x = 360\(^o\)
y = 2 cos 360\(^o\) + 3 sin 360\(^o\)
y = 2
(b)
(c)(i) 1555.5\(^o\), 318\(^o\)
(ii) When x = 3.42\(^o\), y = 0.9\(^o\)