在 $0\le x\le2\pi$ 内解方程

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程；仅给出计算器答案而没有过程，不予评分。除非题目另有精度要求，非精确数值答案保留 3 位有效数字，以度为单位的角度保留 1 位小数。

两边取余弦，先求正弦的两个可能值。注意 $\cos^{-1}$ 给出的角 $2\pi/3$ 在主值范围内。

Taking cosine gives

If $\sin x=-1/2$, then $x=7\pi/6$ or $11\pi/6$. If $\sin x=-1$, then $x=3\pi/2$. For each of these angles, the input to $\cos^{-1}$ is $-1/2$, so they all satisfy the original equation.