tan 正切计算器（tan、cot、反正切，度/弧度）Tangent Calculator (tan, cot, Arctangent, Degrees or Radians)

使用说明与常见问题How-to & FAQ

「正切计算器（tan、cot、反正切，度/弧度）」是什么？What is the Tangent Calculator (tan, cot, Arctangent, Degrees or Radians) tool?

计算角的正切 tan θ 和余切 cot θ，支持度和弧度；常见角会给出精确值（如 tan 30° = √3/3）。也可以反过来由正切值求角度 arctan，或由直角三角形的对边和邻边求 tan 和角度。本地处理。Calculates tan θ and cot θ in degrees or radians, with exact values for common angles (tan 30° = √3/3). Also works backwards with arctan from a tangent value, or from the opposite and adjacent sides of a right triangle. Processed locally.

如何使用「正切计算器（tan、cot、反正切，度/弧度）」？How do I use the Tangent Calculator (tan, cot, Arctangent, Degrees or Radians) tool?

在「正切计算器（tan、cot、反正切，度/弧度）」中，填写「用法」、「角 θ」、「角度单位」、「正切值」、「对边」等参数，结果会随输入实时计算并显示在下方。In the Tangent Calculator (tan, cot, Arctangent, Degrees or Radians): Fill in "Use", "Angle θ", "Angle unit", "Tangent value", "Opposite"; results are recalculated instantly as you type.

正切是什么？What is the tangent?

在直角三角形中，tan θ = 对边 ÷ 邻边；在单位圆上，tan θ = sin θ ÷ cos θ。例如 tan 45° = 1。In a right triangle tan θ = opposite ÷ adjacent; on the unit circle tan θ = sin θ ÷ cos θ. For example tan 45° = 1.

为什么 tan 90° 没有定义？Why is tan 90° undefined?

cos 90° = 0，除以 0 无意义。正切在 90° + k·180° 处有竖直渐近线。cos 90° = 0, and dividing by zero is undefined; tangent has vertical asymptotes at 90° + k·180°.

常见角的精确值Exact values for common angles

tan 0° = 0，tan 30° = √3/3 ≈ 0.577，tan 45° = 1，tan 60° = √3 ≈ 1.732。正切的周期是 180°。tan 0° = 0, tan 30° = √3/3 ≈ 0.577, tan 45° = 1 and tan 60° = √3 ≈ 1.732. Tangent repeats every 180°.

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

例如在「正切计算器（tan、cot、反正切，度/弧度）」中填 θ 度 = 45，结果区显示：tan θ：1For example, entering θ deg = 45 in the Tangent Calculator (tan, cot, Arctangent, Degrees or Radians) gives: tan θ: 1

哪些输入会被检查？Which inputs are validated?

「正切计算器（tan、cot、反正切，度/弧度）」会检查这些输入——「角 θ」、「正切值」：所选方式用到时必须填写；「对边」、「邻边」：所选方式用到时必须填写，须大于 0；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 Tangent Calculator (tan, cot, Arctangent, Degrees or Radians) checks its inputs — "Angle θ", "Tangent value": required when the chosen option uses it; "Opposite", "Adjacent": required when the chosen option uses it, must be greater than 0; 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?

「正切计算器（tan、cot、反正切，度/弧度）」的设置：「用法」可选 由角求 tan、反正切 arctan、由对边和邻边（默认 由角求 tan）；「角 θ」默认 45；「角度单位」可选 度、弧度（默认 度）；「正切值」默认 1；「对边」默认 3；「邻边」默认 4。每次生成结果都按当前设置处理。Settings in the Tangent Calculator (tan, cot, Arctangent, Degrees or Radians) — "Use": tan of an angle, Arctangent, From opposite and adjacent (default tan of an angle); "Angle θ" default 45; "Angle unit": Degrees, Radians (default Degrees); "Tangent value" default 1; "Opposite" default 3; "Adjacent" default 4. The result always uses the current settings.

计算精度如何？How precise are the results?

「正切计算器（tan、cot、反正切，度/弧度）」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 Tangent Calculator (tan, cot, Arctangent, Degrees or Radians) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「正切计算器（tan、cot、反正切，度/弧度）」免费吗？需要注册吗？Is the Tangent Calculator (tan, cot, Arctangent, Degrees or Radians) free? Do I need an account?

「正切计算器（tan、cot、反正切，度/弧度）」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 Tangent Calculator (tan, cot, Arctangent, Degrees or Radians) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.