(a)

x	0°	30°	60°	90°	120°	150°	180°	210°	240°	270°
y	1.0	2.0	2.7	3.0	2.7	2.0	1.0	0.0	-0.7	-1.0

(b)
(c) \(\sin x = \frac{1}{4}\) (Given)
Multiply through by 2 ; \(2 \sin x = 2 \times \frac{1}{4} = \frac{1}{2}\)
\(2 \sin x = \frac{1}{2} \implies 2 \sin x - \frac{1}{2} = 0\)
Add \(1\frac{1}{2}\) to both sides ;
\(2 \sin x - \frac{1}{2} + 1\frac{1}{2} = 0 + 1\frac{1}{2}\)
\(\implies 2 \sin x + 1 = 1\frac{1}{2}\)
Draw the line \(y = 1\frac{1}{2}\) on the same axis as \(y = 2 \sin x + 1\). The line \(y = 1\frac{1}{2}\) cuts the curve at points P and Q where x = 15° and x = 168°. Hence, the values of x for which \(\sin x = \frac{1}{4}\)are 15° and 168°.