WAEC 2020 · Paper 2 · Q6

(a)

Copy and complete the table of values for the relation $y = 3\sin2x$ .

$x$	$0^\circ$	$15^\circ$	$30^\circ$	$45^\circ$	$60^\circ$	$75^\circ$	$90^\circ$	$105^\circ$	$120^\circ$	$135^\circ$	$150^\circ$
$y$	$0.0$					$1.5$					$-2.6$

Model answer

$x$	0°	15°	30°	45°	60°	75°	90°	105°	120°	135°	150°
$y$	0.0	1.5	2.6	3.0	2.6	1.5	0.0	−1.5	−2.6	−3.0	−2.6

For example, at $x = 15^\circ$ : $y = 3\sin30^\circ = 1.5$ .

(b)
Using a scale of 2 cm to $15^\circ$ on the $x$ -axis and 2 cm to 1 unit on the $y$ -axis, draw the graph of $y = 3\sin2x$ for $0^\circ \le x \le 150^\circ$ .
Model answer
Plot every point from the table, then join them with one smooth curve (not straight lines between points). The curve reaches 3 at $45^\circ$ , crosses the axis at $90^\circ$ and reaches $-3$ at $135^\circ$ .

For (c): (i) $3\sin 2x + 2 = 0$ is $y = -2$ : $x \approx 111^\circ$ . (ii) $\frac32\sin 2x = 0.25$ is $3\sin 2x = 0.5$ , so draw $y = 0.5$ : $x \approx 5^\circ$ and $85^\circ$ .
(c)(i)
Use the graph to find the truth set of $3\sin2x + 2 = 0$ .
(c)(ii)
Use the graph to find the truth set of $\frac32\sin2x = 0.25$ .
Separate values with commas, e.g. 3, −2

x in degrees. The lines y = −2 and y = 0.5 give the truth sets.

Worked solution (try it first)

$3\sin 2x + 2 = 0$ is $3\sin 2x = -2$ .
Draw the line $y = -2$ and read where it cuts the curve in this range: $x \approx 111^\circ$ .
The truth set is $\{x : x \approx 111^\circ\}$ .

Multiply both sides of $\frac32\sin 2x = 0.25$ by 2 to match the graph: $3\sin 2x = 0.5$ .
Draw $y = 0.5$ and read where it crosses the curve: $x \approx 5^\circ$ and $x \approx 85^\circ$ .
The truth set is $\{x : x \approx 5^\circ, 85^\circ\}$ .