The graph of $y=\sin x$ for $0^{\circ} \leq x \leq 360^{\circ}$ is shown below. Solve $\sin x=\sin 282^{\circ}$ for $0^{\circ} \leq x \leq 270^{\circ}$

Step 1 ：\(\text{Solve } \sin x = \sin 282^\circ \text{ for } 0^\circ \leq x \leq 270^\circ\)

Step 2 ：\(\text{Use the property of sine function: } \sin(x) = \sin(180 - x) \text{ and } \sin(x) = \sin(360 - x)\)

Step 3 ：\(\sin 282^\circ = -0.9781476007338056\)

Step 4 ：\(x_1 = 258.0^\circ\)

Step 5 ：\(x_2 = 438.0^\circ\)

Step 6 ：\(\text{Only } x_1 \text{ is within the given range}\)

Step 7 ：\(\boxed{x = 258^\circ}\)