(a) Copy and complete the table of values for \(y = 1 - 4\cos x\).
x
0^\circ
30^\circ
60^\circ
90^\circ
120^\circ
150^\circ
180^\circ
210^\circ
240^\circ
270^\circ
300^\circ
y
-3.0
1.0
4.5
-1.0
(b) Using a scale of 2cm to 30^\circ on the x- axis and 2cm to 1 unit on the y- axis, draw the graph of \(y = 1 - 4\cos x\) for \(0^\circ \leq x \leq 360^\circ\).
(c) Use the graph to : (i) solve the equation \(1 - 4\cos x = 0\) ; (ii) find the value of y when x = 105^\circ ; (iii) find x when y = 1.5.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
x
0^\circ
30^\circ
60^\circ
90^\circ
120^\circ
150^\circ
180^\circ
210^\circ
240^\circ
270^\circ
300^\circ
y
-3.0
-2.5
-1.0
1.0
3.0
4.5
5.0
4.5
3.0
1.0
-1.0
(b)
(c)(i) x = 75^\circ or x = 285^\circ
(ii) When x = 105^\circ, y = 2.
(iii) When y = 1.5, x = 96^\circ or x = 264^\circ.
Source: Myschool Past Questions Archive (Record #52730)