(a) x 0^\circ 30^\circ 60^\circ 90^\circ 120^\circ 150^\circ 180^\circ 210^\circ 240^\circ 270^\circ 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^\circ and x = 168^\circ. Hence, the values of x for which \(\sin x = \frac{1}{4}\)are 15^\circ and 168^\circ.