WAEC 2012 · Paper 2 · Q12

(a)

Copy and complete the table of values for $y = 1 - 4\cos x$ .

$x$	$0^\circ$	$30^\circ$	$60^\circ$	$90^\circ$	$120^\circ$	$150^\circ$	$180^\circ$	$210^\circ$	$240^\circ$	$270^\circ$	$300^\circ$
$y$	$-3.0$			$1.0$				$4.5$			$-1.0$

Model answer

$x$	$0^\circ$	$30^\circ$	$60^\circ$	$90^\circ$	$120^\circ$	$150^\circ$	$180^\circ$	$210^\circ$	$240^\circ$	$270^\circ$	$300^\circ$
$y$	$-3.0$	$-2.5$	$-1.0$	$1.0$	$3.0$	$4.5$	$5.0$	$4.5$	$3.0$	$1.0$	$-1.0$

Work to one decimal place in degree mode; for example $x = 60^\circ$ : $1 - 4(0.5) = -1.0$ .

(b)
Using a scale of 2 cm to $30^\circ$ on the $x$ -axis and 2 cm to 1 unit on the $y$ -axis, draw the graph of $y = 1 - 4\cos x$ for $0^\circ \le x \le 300^\circ$ .
Model answer
Plot every point from the table, then join them with one smooth curve (not straight lines between points). Scale: 2 cm to $30^\circ$ , 2 cm to 1 unit. The curve rises from $-3$ at $0^\circ$ to its highest point, 5, at $180^\circ$ .

For (c): (i) it crosses the $x$ -axis at $x \approx 76^\circ$ and $284^\circ$ ; (ii) at $x = 105^\circ$ , $y \approx 2.0$ ; (iii) the line $y = 1.5$ meets it at $x \approx 97^\circ$ and $263^\circ$ .
(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 $y = 1.5$ .
Separate values with commas, e.g. 3, −2

Try it on a graph

x in degrees. The x-axis and the line y = 1.5 give (c)(i) and (c)(iii).

Worked solution (try it first)

(a)

(b)

(c)(i)

$1 - 4\cos x = 0$ is where the curve crosses the line $y = 0$ (the $x$ -axis): $x \approx 76^\circ$ and $x \approx 284^\circ$ .

(ii)

(iii)

Draw the line $y = 1.5$ and read down from where it meets the curve: $x \approx 97^\circ$ and $x \approx 263^\circ$ .