◯ 单位圆计算器（六个三角函数、精确值、象限）Unit Circle Calculator (Six Trig Functions, Exact Values, Quadrant)
输入角度（度、弧度或 π 的倍数，如 3π/4）得到单位圆上的点 (cos θ, sin θ)，以及 tan、sec、csc、cot、所在象限、参考角和 0°–360° 内的同终边角；特殊角给出精确值（如 √2/2）。本地处理。Enter an angle (degrees, radians or a multiple of π such as 3π/4) to get the point (cos θ, sin θ) on the unit circle, plus tan, sec, csc and cot, the quadrant, the reference angle and the coterminal angle in 0°–360°. Special angles get exact values such as √2/2. Processed locally.
使用说明与常见问题How-to & FAQ
「单位圆计算器（六个三角函数、精确值、象限）」是什么？What is the Unit Circle Calculator (Six Trig Functions, Exact Values, Quadrant) tool?
输入角度（度、弧度或 π 的倍数，如 3π/4）得到单位圆上的点 (cos θ, sin θ)，以及 tan、sec、csc、cot、所在象限、参考角和 0°–360° 内的同终边角；特殊角给出精确值（如 √2/2）。本地处理。Enter an angle (degrees, radians or a multiple of π such as 3π/4) to get the point (cos θ, sin θ) on the unit circle, plus tan, sec, csc and cot, the quadrant, the reference angle and the coterminal angle in 0°–360°. Special angles get exact values such as √2/2. Processed locally.
如何使用「单位圆计算器（六个三角函数、精确值、象限）」？How do I use the Unit Circle Calculator (Six Trig Functions, Exact Values, Quadrant) tool?
在「单位圆计算器（六个三角函数、精确值、象限）」中，填写「单位」、「角度 θ」等参数，结果会随输入实时计算并显示在下方。In the Unit Circle Calculator (Six Trig Functions, Exact Values, Quadrant): Fill in "Unit", "Angle θ"; results are recalculated instantly as you type.
单位圆是什么？What is the unit circle?
以原点为圆心、半径为 1 的圆。从正 x 轴逆时针转过角度 θ，落在圆上的点就是 (cos θ, sin θ)，所以 cos² θ + sin² θ = 1。The circle of radius 1 centred at the origin. Turning anticlockwise by θ from the positive x-axis lands on the point (cos θ, sin θ), which is why cos² θ + sin² θ = 1.
怎么输入弧度？How do I enter radians?
选“弧度”，可以输入小数（如 0.7854），也可以写 π 的倍数：π/4、3π/4、-π/6、2π，π 也可以写成 pi。Choose Radians and type a decimal (such as 0.7854) or a multiple of π: π/4, 3π/4, -π/6 or 2π, with pi accepted for π.
什么是参考角？What is the reference angle?
参考角是终边与 x 轴之间的锐角（0°–90°），各象限三角函数的绝对值由它决定，符号由象限决定：第一象限全正，第二象限只有 sin 为正，第三象限只有 tan 为正，第四象限只有 cos 为正。The reference angle is the acute angle (0°–90°) between the terminal side and the x-axis. It fixes the size of each trig value while the quadrant fixes the sign: all positive in I, only sin in II, only tan in III and only cos in IV.
能举个计算实例吗？Can you show a worked example?
例如在「单位圆计算器（六个三角函数、精确值、象限）」中填 单位 = 度，角度 θ = 0，结果区显示：点 (cos θ, sin θ)：(1, 0)；精确值：cos θ = 1, sin θ = 0；tan θ：0；sec θ：1；csc θ：无定义；cot θ：无定义；角度 / 弧度：0° = 0 rad；0°–360° 内的同终边角：0°；象限：在坐标轴上；参考角：0°For example, entering Unit = Degrees, Angle θ = 0 in the Unit Circle Calculator (Six Trig Functions, Exact Values, Quadrant) gives: Point (cos θ, sin θ): (1, 0); Exact values: cos θ = 1, sin θ = 0; tan θ: 0; sec θ: 1; csc θ: not defined; cot θ: not defined; Degrees / radians: 0° = 0 rad; Coterminal angle in 0°–360°: 0°; Quadrant: on an axis; Reference angle: 0°
有哪些选项可以调整？What options can I adjust?
「单位圆计算器（六个三角函数、精确值、象限）」的设置：「单位」可选 度、弧度（可写 π 或 pi，如 3π/4）（默认 度）；「角度 θ」默认 45。每次生成结果都按当前设置处理。Settings in the Unit Circle Calculator (Six Trig Functions, Exact Values, Quadrant) — "Unit": Degrees, Radians (π or pi allowed, e.g. 3π/4) (default Degrees); "Angle θ" default 45. The result always uses the current settings.
计算精度如何？How precise are the results?
「单位圆计算器（六个三角函数、精确值、象限）」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 Unit Circle Calculator (Six Trig Functions, Exact Values, Quadrant) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「单位圆计算器（六个三角函数、精确值、象限）」免费吗？需要注册吗？Is the Unit Circle Calculator (Six Trig Functions, Exact Values, Quadrant) free? Do I need an account?
「单位圆计算器（六个三角函数、精确值、象限）」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 Unit Circle Calculator (Six Trig Functions, Exact Values, Quadrant) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.