(a) Copy and complete the table of values for \(y = 1 - 4\cos x\). x 0° 30° 60° 90° 120° 150° 180° 210° 240° 270° 300° y -3.0 1.0 4.5 -1.0 (b) Using a scale...
Question 1 Report
(a) Copy and complete the table of values for \(y = 1 - 4\cos x\).
| x | 0° | 30° | 60° | 90° | 120° | 150° | 180° | 210° | 240° | 270° | 300° |
| y | -3.0 | 1.0 | 4.5 | -1.0 |
(b) Using a scale of 2cm to 30° on the x- axis and 2cm to 1 unit on the y- axis, draw the graph of \(y = 1 - 4\cos x\) for \(0° \leq x \leq 360°\).
(c) Use the graph to : (i) solve the equation \(1 - 4\cos x = 0\) ; (ii) find the value of y when x = 105° ; (iii) find x when y = 1.5.
Answer Details
(a) For each value of x, calculate \(y=1-4\cos x\), correct to 1 decimal place.
| \(x\) | \(0^\circ\) | \(30^\circ\) | \(60^\circ\) | \(90^\circ\) | \(120^\circ\) | \(150^\circ\) | \(180^\circ\) | \(210^\circ\) | \(240^\circ\) | \(270^\circ\) | \(300^\circ\) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(y\) | -3.0 | -2.5 | -1.0 | 1.0 | 3.0 | 4.5 | 5.0 | 4.5 | 3.0 | 1.0 | -1.0 |
(b) The completed graph of \(y=1-4\cos x\), including \(y=-2.5\) at \(330^\circ\) and \(y=-3.0\) at \(360^\circ\), is shown below.
(c)
(i) The points where the curve cuts the \(x\)-axis give
\[x\approx75^\circ\quad\text{or}\quad285^\circ.\]
(ii) At \(x=105^\circ\), the ordinate of the curve is
\[y\approx2.0.\]
(iii) Drawing the horizontal line \(y=1.5\) and reading the two intersections with the curve gives
\[x\approx96^\circ\quad\text{or}\quad264^\circ.\]
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