trig 余函数计算器（sin/cos、tan/cot、sec/csc）Cofunction Calculator (sin/cos, tan/cot, sec/csc)

使用说明与常见问题How-to & FAQ

「余函数计算器（sin/cos、tan/cot、sec/csc）」是什么？What is the Cofunction Calculator (sin/cos, tan/cot, sec/csc) tool?

输入角度（度或弧度，弧度可写 π），把六种三角函数写成余函数形式，例如 sin θ = cos(90° − θ)，并给出两边的数值以便核对。本地处理。Enter an angle in degrees or radians (π allowed) to rewrite any of the six trig functions as its cofunction, such as sin θ = cos(90° − θ), with the value of both sides so you can check them. Processed locally.

如何使用「余函数计算器（sin/cos、tan/cot、sec/csc）」？How do I use the Cofunction Calculator (sin/cos, tan/cot, sec/csc) tool?

在「余函数计算器（sin/cos、tan/cot、sec/csc）」中，填写「函数」、「角度 θ」、「单位」等参数，结果会随输入实时计算并显示在下方。In the Cofunction Calculator (sin/cos, tan/cot, sec/csc): Fill in "Function", "Angle θ", "Unit"; results are recalculated instantly as you type.

什么是余函数？What are cofunctions?

sin 和 cos、tan 和 cot、sec 和 csc 互为余函数：一个角的函数值等于它的余角（90° − θ）的余函数值，例如 sin θ = cos(90° − θ)、tan θ = cot(90° − θ)。sin and cos, tan and cot, and sec and csc are cofunction pairs: a function of an angle equals its cofunction of the complementary angle 90° − θ, for example sin θ = cos(90° − θ) and tan θ = cot(90° − θ).

弧度怎么写？How do I write radians?

选择弧度后可以输入小数（如 0.5236）或带 π 的形式（如 π/6、2π/3、pi/4）。90° 对应 π/2。Choose radians and type a decimal such as 0.5236 or a form with π such as π/6, 2π/3 or pi/4. 90° is π/2.

为什么有时显示无定义？Why does it sometimes say undefined?

tan、sec 在 90° 的奇数倍处无定义，cot、csc 在 0°、180° 等处无定义，因为分母为 0。tan and sec are undefined at odd multiples of 90°, and cot and csc at 0°, 180° and so on, because the denominator is 0.

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

例如在「余函数计算器（sin/cos、tan/cot、sec/csc）」中填 函数 = sin，角度 θ = 30，单位 = 度，结果区显示：余函数关系：sin θ = cos(90° − θ)；代入：sin(30°) = cos(90° − 30°) = cos(60°)；sin θ：0.5；cos(90° − θ)：0.5For example, entering Function = sin, Angle θ = 30, Unit = Degrees in the Cofunction Calculator (sin/cos, tan/cot, sec/csc) gives: Cofunction identity: sin θ = cos(90° − θ); Substituted: sin(30°) = cos(90° − 30°) = cos(60°); sin θ: 0.5; cos(90° − θ): 0.5

有哪些选项可以调整？What options can I adjust?

「余函数计算器（sin/cos、tan/cot、sec/csc）」的设置：「函数」可选 sin、cos、tan、cot、sec、csc（默认 sin）；「角度 θ」默认 30；「单位」可选 度、弧度（默认 度）。每次生成结果都按当前设置处理。Settings in the Cofunction Calculator (sin/cos, tan/cot, sec/csc) — "Function": sin, cos, tan, cot, sec, csc (default sin); "Angle θ" default 30; "Unit": Degrees, Radians (default Degrees). The result always uses the current settings.

计算精度如何？How precise are the results?

「余函数计算器（sin/cos、tan/cot、sec/csc）」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 Cofunction Calculator (sin/cos, tan/cot, sec/csc) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「余函数计算器（sin/cos、tan/cot、sec/csc）」免费吗？需要注册吗？Is the Cofunction Calculator (sin/cos, tan/cot, sec/csc) free? Do I need an account?

「余函数计算器（sin/cos、tan/cot、sec/csc）」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 Cofunction Calculator (sin/cos, tan/cot, sec/csc) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.