cos 余弦计算器（含 sin、tan、arccos 与余弦定理）Cosine Calculator (with sin, tan, arccos & Law of Cosines)
计算 cos θ（也可选 sin、tan），或由余弦值求角度（arccos），或用余弦定理求三角形的边或角。角度可用度或弧度，弧度可直接写 pi/2 这样的表达式；90°、270°、π/2 等特殊角给出精确的 0。本地处理。Compute cos θ (or sin and tan), the angle for a cosine value (arccos), or a side or angle of a triangle with the law of cosines. Angles in degrees or radians, and radians can be written as expressions such as pi/2; special angles such as 90°, 270° and π/2 give an exact 0. Processed locally.
使用说明与常见问题How-to & FAQ
「余弦计算器（含 sin、tan、arccos 与余弦定理）」是什么？What is the Cosine Calculator (with sin, tan, arccos & Law of Cosines) tool?
计算 cos θ（也可选 sin、tan），或由余弦值求角度（arccos），或用余弦定理求三角形的边或角。角度可用度或弧度，弧度可直接写 pi/2 这样的表达式；90°、270°、π/2 等特殊角给出精确的 0。本地处理。Compute cos θ (or sin and tan), the angle for a cosine value (arccos), or a side or angle of a triangle with the law of cosines. Angles in degrees or radians, and radians can be written as expressions such as pi/2; special angles such as 90°, 270° and π/2 give an exact 0. Processed locally.
如何使用「余弦计算器（含 sin、tan、arccos 与余弦定理）」？How do I use the Cosine Calculator (with sin, tan, arccos & Law of Cosines) tool?
在「余弦计算器（含 sin、tan、arccos 与余弦定理）」中，填写「计算」、「角度单位」、「θ（角度；arccos 模式为余弦值）」、「边 a」、「边 b」等参数，结果会随输入实时计算并显示在下方。In the Cosine Calculator (with sin, tan, arccos & Law of Cosines): Fill in "Calculate", "Angle unit", "θ (angle; cosine value in arccos mode)", "Side a", "Side b"; results are recalculated instantly as you type.
为什么 cos 90° 显示 0？Why does cos 90° show exactly 0?
在浮点数里 π/2 不能精确表示，直接计算 cos(π/2) 会得到 6.1×10⁻¹⁷ 这样的“噪声”。本页对 90° 的整数倍直接使用精确值，并把绝对值小于 10⁻¹² 的结果视为 0，所以 cos 90°、cos 270° 和 cos(pi/2) 都显示 0。π/2 cannot be stored exactly in floating point, so a plain cos(π/2) gives noise such as 6.1×10⁻¹⁷. The page uses exact values for multiples of 90° and treats results smaller than 10⁻¹² as 0, so cos 90°, cos 270° and cos(pi/2) all show 0.
θ 可以怎么写？How can I write θ?
可以是普通数字，也可以是表达式，例如 pi/2、2*pi/3 或 45+30。默认单位是度，选弧度后按弧度理解。θ 必须填写。A plain number or an expression such as pi/2, 2*pi/3 or 45+30. Degrees are the default; choose radians to read it in radians. θ is required.
余弦定理怎么用？How do I use the law of cosines?
求边：c² = a² + b² − 2ab·cos C，例如 a = 3、b = 4、C = 90° 时 c = 5。求角：cos C = (a² + b² − c²) ÷ 2ab，例如三边 3、4、5 时 C = 90°。三边须满足任意两边之和大于第三边。For a side: c² = a² + b² − 2ab·cos C, so a = 3, b = 4 and C = 90° give c = 5. For an angle: cos C = (a² + b² − c²) ÷ 2ab, so sides 3, 4 and 5 give C = 90°. Any two sides must add up to more than the third.
arccos 的结果范围？What range does arccos give?
输入 −1 到 1 之间的余弦值，结果是 0° 到 180° 之间的主值，同时给出弧度。Enter a cosine value between −1 and 1; the result is the principal value from 0° to 180°, also shown in radians.
能举个计算实例吗？Can you show a worked example?
例如在「余弦计算器（含 sin、tan、arccos 与余弦定理）」中填 计算 = cos θ / cos θ，角度单位 = 度，θ（角度；arccos 模式为余弦值） = 60，边 a = 3，边 b = 4，边 c（求角时） = 5，结果区显示：θ：60°；cos θ：0.5For example, entering Calculate = cos θ / cos θ, Angle unit = Degrees, θ (angle; cosine value in arccos mode) = 60, Side a = 3, Side b = 4, Side c (for the angle) = 5 in the Cosine Calculator (with sin, tan, arccos & Law of Cosines) gives: θ: 60°; cos θ: 0.5
哪些输入会被检查？Which inputs are validated?
「余弦计算器（含 sin、tan、arccos 与余弦定理）」会检查这些输入——「边 a」、「边 b」、「边 c（求角时）」：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 Cosine Calculator (with sin, tan, arccos & Law of Cosines) checks its inputs — "Side a", "Side b", "Side c (for the angle)": required, 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?
「余弦计算器（含 sin、tan、arccos 与余弦定理）」的设置：「计算」可选 cos θ / cos θ、sin θ / sin θ、tan θ / tan θ、由余弦值求角度（arccos）、余弦定理：由 a、b 和夹角 C 求边 c、余弦定理：由三边求角 C（默认 cos θ / cos θ）；「角度单位」可选 度、弧度（默认 度）；「θ（角度；arccos 模式为余弦值）」默认 60；「边 a」默认 3；「边 b」默认 4；「边 c（求角时）」默认 5；「夹角 C（求边时）」默认 90。每次生成结果都按当前设置处理。Settings in the Cosine Calculator (with sin, tan, arccos & Law of Cosines) — "Calculate": cos θ / cos θ, sin θ / sin θ, tan θ / tan θ, Angle from a cosine (arccos), Law of cosines: side c from a, b and angle C, Law of cosines: angle C from three sides (default cos θ / cos θ); "Angle unit": Degrees, Radians (default Degrees); "θ (angle; cosine value in arccos mode)" default 60; "Side a" default 3; "Side b" default 4; "Side c (for the angle)" default 5; "Angle C (for the side)" default 90. The result always uses the…
计算精度如何？How precise are the results?
「余弦计算器（含 sin、tan、arccos 与余弦定理）」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 Cosine Calculator (with sin, tan, arccos & Law of Cosines) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「余弦计算器（含 sin、tan、arccos 与余弦定理）」免费吗？需要注册吗？Is the Cosine Calculator (with sin, tan, arccos & Law of Cosines) free? Do I need an account?
「余弦计算器（含 sin、tan、arccos 与余弦定理）」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 Cosine Calculator (with sin, tan, arccos & Law of Cosines) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.