(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\(^o\)
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(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\(^o\)
Source: Myschool Past Questions Archive (Record #58147)