∠ 参考角计算器（度、弧度、象限、同终边角）Reference Angle Calculator (Degrees, Radians, Quadrant, Coterminal Angles)

使用说明与常见问题How-to & FAQ

「参考角计算器（度、弧度、象限、同终边角）」是什么？What is the Reference Angle Calculator (Degrees, Radians, Quadrant, Coterminal Angles) tool?

把任意角（可为负数或大于 360°）化到 0–90° 的参考角，支持度、弧度和 π 弧度输入。同时给出 0–360° 内的同终边角、所在象限或坐标轴，以及 sin、cos、tan 在该象限的符号。本地处理。Reduces any angle (negative or above 360°) to its reference angle between 0 and 90°, with degrees, radians or multiples of π as input. Also gives the coterminal angle in 0–360°, the quadrant or axis, and the signs of sin, cos and tan there. Processed locally.

如何使用「参考角计算器（度、弧度、象限、同终边角）」？How do I use the Reference Angle Calculator (Degrees, Radians, Quadrant, Coterminal Angles) tool?

在「参考角计算器（度、弧度、象限、同终边角）」中，填写「角度」、「单位」、「π 的倍数（分数或小数）」等参数，结果会随输入实时计算并显示在下方。In the Reference Angle Calculator (Degrees, Radians, Quadrant, Coterminal Angles): Fill in "Angle", "Unit", "Multiple of π (fraction or decimal)"; results are recalculated instantly as you type.

参考角怎么求？How do I find a reference angle?

先把角化到 0–360° 之间，再看象限：第一象限就是它本身；第二象限 180° − θ；第三象限 θ − 180°；第四象限 360° − θ。Bring the angle into 0–360°, then by quadrant: quadrant I is the angle itself, II is 180° − θ, III is θ − 180° and IV is 360° − θ.

负角怎么处理？What about negative angles?

加上 360° 的整数倍直到落在 0–360° 内。例如 −210° + 360° = 150°，参考角是 30°。Add multiples of 360° until it lies in 0–360°. −210° + 360° = 150°, whose reference angle is 30°.

参考角有什么用？What is the reference angle for?

任意角的三角函数值等于其参考角的函数值，再按象限加正负号（“全正、正弦、正切、余弦”规律）。Any angle's trig values equal those of its reference angle with the sign set by the quadrant (the All Students Take Calculus rule).

能举个计算实例吗？Can you show a worked example?

例如在「参考角计算器（度、弧度、象限、同终边角）」中填 角度 = 150，单位 = 度，结果区显示：参考角 °：30；参考角（弧度）：0.52359878 = π/6；同终边角（0–360°）：150°；所在位置：第二象限；符号 sin / cos / tan：+ / − / −；其他同终边角：-570°, -210°, 510°, 870°For example, entering Angle = 150, Unit = Degrees in the Reference Angle Calculator (Degrees, Radians, Quadrant, Coterminal Angles) gives: Reference °: 30; Reference angle (radians): 0.52359878 = π/6; Coterminal angle (0–360°): 150°; Position: quadrant II; Signs of sin / cos / tan: + / − / −; Other coterminal angles: -570°, -210°, 510°, 870°

哪些输入会被检查？Which inputs are validated?

「参考角计算器（度、弧度、象限、同终边角）」会检查这些输入——「角度」：所选方式用到时必须填写；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Reference Angle Calculator (Degrees, Radians, Quadrant, Coterminal Angles) checks its inputs — "Angle": required when the chosen option uses it; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「参考角计算器（度、弧度、象限、同终边角）」的设置：「角度」默认 150；「单位」可选 度、弧度、π 的倍数（如 5/6）（默认 度）；「π 的倍数（分数或小数）」默认 5/6。每次生成结果都按当前设置处理。Settings in the Reference Angle Calculator (Degrees, Radians, Quadrant, Coterminal Angles) — "Angle" default 150; "Unit": Degrees, Radians, Multiple of π (such as 5/6) (default Degrees); "Multiple of π (fraction or decimal)" default 5/6. The result always uses the current settings.

计算精度如何？How precise are the results?

「参考角计算器（度、弧度、象限、同终边角）」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Reference Angle Calculator (Degrees, Radians, Quadrant, Coterminal Angles) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「参考角计算器（度、弧度、象限、同终边角）」免费吗？需要注册吗？Is the Reference Angle Calculator (Degrees, Radians, Quadrant, Coterminal Angles) free? Do I need an account?

「参考角计算器（度、弧度、象限、同终边角）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Reference Angle Calculator (Degrees, Radians, Quadrant, Coterminal Angles) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.