反余弦计算器

输入余弦值，计算对应的角度和弧度。

反余弦计算

角度

弧度

什么是反余弦函数

反余弦函数（Arccosine function）是余弦函数的反函数，通常用符号 \(\arccos(x)\) 或 \(\cos^{-1}(x)\) 表示，用于求出给定余弦值对应的角度。对于余弦函数 \(y = \cos(\theta)\)，反余弦函数定义为： \( \theta = \arccos(x) \) 其中，\(-1 \leq x \leq 1\) 且 \(0 \leq \theta \leq \pi\)。反余弦的值域为 \([0, \pi]\)，这是为了确保反余弦函数唯一且可逆。

示例

例子 1：已知 \(\cos(\theta) = 0\)，求对应的角度 \(\theta\)：

解答：

\( \theta = \arccos(0) = \frac{\pi}{2} \approx 1.5708 \, \text{弧度} \)

因此，余弦值为 0 的角度是 \(\frac{\pi}{2}\) 或 90°。

例子 2：假设已知 \(\cos(\theta) = 0.5\)，求对应的角度 \(\theta\)：

解答：

\( \theta = \arccos(0.5) = \frac{\pi}{3} \approx 1.0472 \, \text{弧度} \)

因此，余弦值为 0.5 的角度是 \(\frac{\pi}{3}\) 或 60°。

反余弦函数的图形

arccosine graph

反余弦函数的图形是从 \((1, 0)\) 到 \((-1, \pi)\) 的递减曲线。其定义域为 \([-1, 1]\)，值域为 \([0, \pi]\)。在定义域内，反余弦函数是单调递减的；不具有奇偶性。

反余弦函数转换表格

余弦值 角度 弧度
10°0
0.99984771°\(\frac{\pi}{180}\)
0.999390832°\(\frac{\pi}{90}\)
0.998629533°\(\frac{\pi}{60}\)
0.997564054°\(\frac{\pi}{45}\)
0.99619475°\(\frac{\pi}{36}\)
0.99452196°\(\frac{\pi}{30}\)
0.992546157°\(\frac{7\pi}{180}\)
0.990268078°\(\frac{2\pi}{45}\)
0.987688349°\(\frac{\pi}{20}\)
0.9848077510°\(\frac{\pi}{18}\)
0.9816271811°\(\frac{11\pi}{180}\)
0.978147612°\(\frac{\pi}{15}\)
0.9743700613°\(\frac{13\pi}{180}\)
0.9702957314°\(\frac{7\pi}{90}\)
0.9659258315°\(\frac{\pi}{12}\)
0.961261716°\(\frac{4\pi}{45}\)
0.9563047617°\(\frac{17\pi}{180}\)
0.9510565218°\(\frac{\pi}{10}\)
0.9455185819°\(\frac{19\pi}{180}\)
0.9396926220°\(\frac{\pi}{9}\)
0.9335804321°\(\frac{7\pi}{60}\)
0.9271838522°\(\frac{11\pi}{90}\)
0.9205048523°\(\frac{23\pi}{180}\)
0.9135454624°\(\frac{2\pi}{15}\)
0.9063077925°\(\frac{5\pi}{36}\)
0.8987940526°\(\frac{13\pi}{90}\)
0.8910065227°\(\frac{3\pi}{20}\)
0.8829475928°\(\frac{7\pi}{45}\)
0.8746197129°\(\frac{29\pi}{180}\)
0.866025430°\(\frac{\pi}{6}\)
0.857167331°\(\frac{31\pi}{180}\)
0.848048132°\(\frac{8\pi}{45}\)
0.8386705733°\(\frac{11\pi}{60}\)
0.8290375734°\(\frac{17\pi}{90}\)
0.8191520435°\(\frac{7\pi}{36}\)
0.8090169936°\(\frac{\pi}{5}\)
0.7986355137°\(\frac{37\pi}{180}\)
0.7880107538°\(\frac{19\pi}{90}\)
0.7771459639°\(\frac{13\pi}{60}\)
0.7660444440°\(\frac{2\pi}{9}\)
0.7547095841°\(\frac{41\pi}{180}\)
0.7431448342°\(\frac{7\pi}{30}\)
0.731353743°\(\frac{43\pi}{180}\)
0.719339844°\(\frac{11\pi}{45}\)
0.7071067845°\(\frac{\pi}{4}\)
0.6946583746°\(\frac{23\pi}{90}\)
0.6819983647°\(\frac{47\pi}{180}\)
0.6691306148°\(\frac{4\pi}{15}\)
0.6560590349°\(\frac{49\pi}{180}\)
0.6427876150°\(\frac{5\pi}{18}\)
0.6293203951°\(\frac{17\pi}{60}\)
0.6156614852°\(\frac{13\pi}{45}\)
0.6018150253°\(\frac{53\pi}{180}\)
0.5877852554°\(\frac{3\pi}{10}\)
0.5735764455°\(\frac{11\pi}{36}\)
0.559192956°\(\frac{14\pi}{45}\)
0.5446390457°\(\frac{19\pi}{60}\)
0.5299192658°\(\frac{29\pi}{90}\)
0.5150380759°\(\frac{59\pi}{180}\)
0.560°\(\frac{\pi}{3}\)
0.4848096261°\(\frac{61\pi}{180}\)
0.4694715662°\(\frac{31\pi}{90}\)
0.453990563°\(\frac{7\pi}{20}\)
0.4383711564°\(\frac{16\pi}{45}\)
0.4226182665°\(\frac{13\pi}{36}\)
0.4067366466°\(\frac{11\pi}{30}\)
0.3907311367°\(\frac{67\pi}{180}\)
0.3746065968°\(\frac{17\pi}{45}\)
0.3583679569°\(\frac{23\pi}{60}\)
0.3420201470°\(\frac{7\pi}{18}\)
0.3255681571°\(\frac{71\pi}{180}\)
0.3090169972°\(\frac{2\pi}{5}\)
0.292371773°\(\frac{73\pi}{180}\)
0.2756373674°\(\frac{37\pi}{90}\)
0.2588190575°\(\frac{5\pi}{12}\)
0.241921976°\(\frac{19\pi}{45}\)
0.2249510577°\(\frac{77\pi}{180}\)
0.2079116978°\(\frac{13\pi}{30}\)
0.19080979°\(\frac{79\pi}{180}\)
0.1736481880°\(\frac{4\pi}{9}\)
0.1564344781°\(\frac{9\pi}{20}\)
0.139173182°\(\frac{41\pi}{90}\)
0.1218693483°\(\frac{83\pi}{180}\)
0.1045284684°\(\frac{7\pi}{15}\)
0.0871557485°\(\frac{17\pi}{36}\)
0.0697564786°\(\frac{43\pi}{90}\)
0.0523359687°\(\frac{29\pi}{60}\)
0.034899588°\(\frac{22\pi}{45}\)
0.0174524189°\(\frac{89\pi}{180}\)
090°\(\frac{\pi}{2}\)
-0.0174524191°\(\frac{91\pi}{180}\)
-0.034899592°\(\frac{23\pi}{45}\)
-0.0523359693°\(\frac{31\pi}{60}\)
-0.0697564794°\(\frac{47\pi}{90}\)
-0.0871557495°\(\frac{19\pi}{36}\)
-0.1045284696°\(\frac{8\pi}{15}\)
-0.1218693497°\(\frac{97\pi}{180}\)
-0.139173198°\(\frac{49\pi}{90}\)
-0.1564344799°\(\frac{11\pi}{20}\)
-0.17364818100°\(\frac{5\pi}{9}\)
-0.190809101°\(\frac{101\pi}{180}\)
-0.20791169102°\(\frac{17\pi}{30}\)
-0.22495105103°\(\frac{103\pi}{180}\)
-0.2419219104°\(\frac{26\pi}{45}\)
-0.25881905105°\(\frac{7\pi}{12}\)
-0.27563736106°\(\frac{53\pi}{90}\)
-0.2923717107°\(\frac{107\pi}{180}\)
-0.30901699108°\(\frac{3\pi}{5}\)
-0.32556815109°\(\frac{109\pi}{180}\)
-0.34202014110°\(\frac{11\pi}{18}\)
-0.35836795111°\(\frac{37\pi}{60}\)
-0.37460659112°\(\frac{28\pi}{45}\)
-0.39073113113°\(\frac{113\pi}{180}\)
-0.40673664114°\(\frac{19\pi}{30}\)
-0.42261826115°\(\frac{23\pi}{36}\)
-0.43837115116°\(\frac{29\pi}{45}\)
-0.4539905117°\(\frac{13\pi}{20}\)
-0.46947156118°\(\frac{59\pi}{90}\)
-0.48480962119°\(\frac{119\pi}{180}\)
-0.5120°\(\frac{2\pi}{3}\)
-0.51503807121°\(\frac{121\pi}{180}\)
-0.52991926122°\(\frac{61\pi}{90}\)
-0.54463904123°\(\frac{41\pi}{60}\)
-0.5591929124°\(\frac{31\pi}{45}\)
-0.57357644125°\(\frac{25\pi}{36}\)
-0.58778525126°\(\frac{7\pi}{10}\)
-0.60181502127°\(\frac{127\pi}{180}\)
-0.61566148128°\(\frac{32\pi}{45}\)
-0.62932039129°\(\frac{43\pi}{60}\)
-0.64278761130°\(\frac{13\pi}{18}\)
-0.65605903131°\(\frac{131\pi}{180}\)
-0.66913061132°\(\frac{11\pi}{15}\)
-0.68199836133°\(\frac{133\pi}{180}\)
-0.69465837134°\(\frac{67\pi}{90}\)
-0.70710678135°\(\frac{3\pi}{4}\)
-0.7193398136°\(\frac{34\pi}{45}\)
-0.7313537137°\(\frac{137\pi}{180}\)
-0.74314483138°\(\frac{23\pi}{30}\)
-0.75470958139°\(\frac{139\pi}{180}\)
-0.76604444140°\(\frac{7\pi}{9}\)
-0.77714596141°\(\frac{47\pi}{60}\)
-0.78801075142°\(\frac{71\pi}{90}\)
-0.79863551143°\(\frac{143\pi}{180}\)
-0.80901699144°\(\frac{4\pi}{5}\)
-0.81915204145°\(\frac{29\pi}{36}\)
-0.82903757146°\(\frac{73\pi}{90}\)
-0.83867057147°\(\frac{49\pi}{60}\)
-0.8480481148°\(\frac{37\pi}{45}\)
-0.8571673149°\(\frac{149\pi}{180}\)
-0.8660254150°\(\frac{5\pi}{6}\)
-0.87461971151°\(\frac{151\pi}{180}\)
-0.88294759152°\(\frac{38\pi}{45}\)
-0.89100652153°\(\frac{17\pi}{20}\)
-0.89879405154°\(\frac{77\pi}{90}\)
-0.90630779155°\(\frac{31\pi}{36}\)
-0.91354546156°\(\frac{13\pi}{15}\)
-0.92050485157°\(\frac{157\pi}{180}\)
-0.92718385158°\(\frac{79\pi}{90}\)
-0.93358043159°\(\frac{53\pi}{60}\)
-0.93969262160°\(\frac{8\pi}{9}\)
-0.94551858161°\(\frac{161\pi}{180}\)
-0.95105652162°\(\frac{9\pi}{10}\)
-0.95630476163°\(\frac{163\pi}{180}\)
-0.9612617164°\(\frac{41\pi}{45}\)
-0.96592583165°\(\frac{11\pi}{12}\)
-0.97029573166°\(\frac{83\pi}{90}\)
-0.97437006167°\(\frac{167\pi}{180}\)
-0.9781476168°\(\frac{14\pi}{15}\)
-0.98162718169°\(\frac{169\pi}{180}\)
-0.98480775170°\(\frac{17\pi}{18}\)
-0.98768834171°\(\frac{19\pi}{20}\)
-0.99026807172°\(\frac{43\pi}{45}\)
-0.99254615173°\(\frac{173\pi}{180}\)
-0.9945219174°\(\frac{29\pi}{30}\)
-0.9961947175°\(\frac{35\pi}{36}\)
-0.99756405176°\(\frac{44\pi}{45}\)
-0.99862953177°\(\frac{59\pi}{60}\)
-0.99939083178°\(\frac{89\pi}{90}\)
-0.9998477179°\(\frac{179\pi}{180}\)
-1180°π
相关计算器

反正弦计算器

反余割计算器

反正割计算器

反正切计算器

最新计算器

等边三角形计算器

距离计算器

中点计算器

黄金比例计算器

中位数绝对偏差计算器

热门计算器

出勤率与缺勤率计算器

圆心角计算器

扇形半径计算器

质数总和计算器

欧拉函数计算器

根据两个数的总和与积找数