三角函数
三角函数的基本定义
编辑三角函数最一开始是用来表示角度和直角三角形三边边长关系的式子,直角三角形中的 和可由毕氏定理给出它的定义: 若一个直角三角形,它的一个锐角角度为,此角的对边为,邻边为,斜边为(如图所示),则:
因此得到正弦函数和馀弦函数的定义.
当时,且
弧度制与角度制的转换
编辑一个角度制数值所对应的弧度制数值等于单位圆中圆心角角度与该角度制数值相同时该圆心角所对应的弧长。用表示弧度制数值,用表示角度制数值,二者转换关系为:
常用的弧度转换公式:
主要的公式
编辑倒数关系
编辑
平方相加
编辑
和角公式
编辑
倍角公式 & 半角公式
编辑2倍角公式:
3倍角公式:
半角公式:
积化和差:
和差化积:
其他公式
编辑万能公式:
平方差公式:
降次升角公式:
辅助角公式:
三角函数的一些进阶定理
编辑正弦定理:
编辑若为任意三角形的三边,,,,,分别为,,的对角,为此三角形的外接圆半径,则存有以下关系式:
由勾股定理得 当的终边与坐标轴重合时,这个公式也成立。
根据三角函数的定义,当()时,有
这就是说,同一个角的正弦、余弦的平方和等于1,商等于角的正切。
三角分析
编辑面积公式:
三角形形状的判定:
1) 为三角形最大边时
三角形为直角三角形
三角形为锐角三角形
三角形为钝角三角形
2) 推出
三角函数应用
编辑三角测量
编辑其他应用
编辑附录表
编辑附录─三角函数表
编辑度 | 分 | sin | cos | tan | cot | sec | csc | 度 | 分 |
0 | 00 | 0.0000 | 1.0000 | 0.0000 | 未定义 | 1.0000 | 未定义 | 90 | 00 |
0 | 10 | 0.0029 | 1.0000 | 0.0029 | 343.7737 | 1.0000 | 343.7752 | 89 | 50 |
0 | 20 | 0.0058 | 1.0000 | 0.0058 | 171.8854 | 1.0000 | 171.8883 | 89 | 40 |
0 | 30 | 0.0087 | 1.0000 | 0.0087 | 114.5887 | 1.0000 | 114.5930 | 89 | 30 |
0 | 40 | 0.0116 | 0.9999 | 0.0116 | 85.9398 | 1.0001 | 85.9456 | 89 | 20 |
0 | 50 | 0.0145 | 0.9999 | 0.0145 | 68.7501 | 1.0001 | 68.7574 | 89 | 10 |
1 | 00 | 0.0175 | 0.9998 | 0.0175 | 57.2900 | 1.0002 | 57.2987 | 89 | 00 |
1 | 10 | 0.0204 | 0.9998 | 0.0204 | 49.1039 | 1.0002 | 49.1141 | 88 | 50 |
1 | 20 | 0.0233 | 0.9997 | 0.0233 | 42.9641 | 1.0003 | 42.9757 | 88 | 40 |
1 | 30 | 0.0262 | 0.9997 | 0.0262 | 38.1885 | 1.0003 | 38.2016 | 88 | 30 |
1 | 40 | 0.0291 | 0.9996 | 0.0291 | 34.3678 | 1.0004 | 34.3823 | 88 | 20 |
1 | 50 | 0.0320 | 0.9995 | 0.0320 | 31.2416 | 1.0005 | 31.2576 | 88 | 10 |
2 | 00 | 0.0349 | 0.9994 | 0.0349 | 28.6363 | 1.0006 | 28.6537 | 88 | 00 |
2 | 10 | 0.0378 | 0.9993 | 0.0378 | 26.4316 | 1.0007 | 26.4505 | 87 | 50 |
2 | 20 | 0.0407 | 0.9992 | 0.0407 | 24.5418 | 1.0008 | 24.5621 | 87 | 40 |
2 | 30 | 0.0436 | 0.9990 | 0.0437 | 22.9038 | 1.0010 | 22.9256 | 87 | 30 |
2 | 40 | 0.0465 | 0.9989 | 0.0466 | 21.4704 | 1.0011 | 21.4937 | 87 | 20 |
2 | 50 | 0.0494 | 0.9988 | 0.0495 | 20.2056 | 1.0012 | 20.2303 | 87 | 10 |
3 | 00 | 0.0523 | 0.9986 | 0.0524 | 19.0811 | 1.0014 | 19.1073 | 87 | 00 |
3 | 10 | 0.0552 | 0.9985 | 0.0553 | 18.0750 | 1.0015 | 18.1026 | 86 | 50 |
3 | 20 | 0.0581 | 0.9983 | 0.0582 | 17.1693 | 1.0017 | 17.1984 | 86 | 40 |
3 | 30 | 0.0610 | 0.9981 | 0.0612 | 16.3499 | 1.0019 | 16.3804 | 86 | 30 |
3 | 40 | 0.0640 | 0.9980 | 0.0641 | 15.6048 | 1.0021 | 15.6368 | 86 | 20 |
3 | 50 | 0.0669 | 0.9978 | 0.0670 | 14.9244 | 1.0022 | 14.9579 | 86 | 10 |
4 | 00 | 0.0698 | 0.9976 | 0.0699 | 14.3007 | 1.0024 | 14.3356 | 86 | 00 |
4 | 10 | 0.0727 | 0.9974 | 0.0729 | 13.7267 | 1.0027 | 13.7631 | 85 | 50 |
4 | 20 | 0.0756 | 0.9971 | 0.0758 | 13.1969 | 1.0029 | 13.2347 | 85 | 40 |
4 | 30 | 0.0785 | 0.9969 | 0.0787 | 12.7062 | 1.0031 | 12.7455 | 85 | 30 |
4 | 40 | 0.0814 | 0.9967 | 0.0816 | 12.2505 | 1.0033 | 12.2913 | 85 | 20 |
4 | 50 | 0.0843 | 0.9964 | 0.0846 | 11.8262 | 1.0036 | 11.8684 | 85 | 10 |
5 | 00 | 0.0872 | 0.9962 | 0.0875 | 11.4301 | 1.0038 | 11.4737 | 85 | 00 |
5 | 10 | 0.0901 | 0.9959 | 0.0904 | 11.0594 | 1.0041 | 11.1045 | 84 | 50 |
5 | 20 | 0.0929 | 0.9957 | 0.0934 | 10.7119 | 1.0043 | 10.7585 | 84 | 40 |
5 | 30 | 0.0958 | 0.9954 | 0.0963 | 10.3854 | 1.0046 | 10.4334 | 84 | 30 |
5 | 40 | 0.0987 | 0.9951 | 0.0992 | 10.0780 | 1.0049 | 10.1275 | 84 | 20 |
5 | 50 | 0.1016 | 0.9948 | 0.1022 | 9.7882 | 1.0052 | 9.8391 | 84 | 10 |
6 | 00 | 0.1045 | 0.9945 | 0.1051 | 9.5144 | 1.0055 | 9.5668 | 84 | 00 |
6 | 10 | 0.1074 | 0.9942 | 0.1080 | 9.2553 | 1.0058 | 9.3092 | 83 | 50 |
6 | 20 | 0.1103 | 0.9939 | 0.1110 | 9.0098 | 1.0061 | 9.0652 | 83 | 40 |
6 | 30 | 0.1132 | 0.9936 | 0.1139 | 8.7769 | 1.0065 | 8.8337 | 83 | 30 |
6 | 40 | 0.1161 | 0.9932 | 0.1169 | 8.5555 | 1.0068 | 8.6138 | 83 | 20 |
6 | 50 | 0.1190 | 0.9929 | 0.1198 | 8.3450 | 1.0072 | 8.4047 | 83 | 10 |
7 | 00 | 0.1219 | 0.9925 | 0.1228 | 8.1443 | 1.0075 | 8.2055 | 83 | 00 |
7 | 10 | 0.1248 | 0.9922 | 0.1257 | 7.9530 | 1.0079 | 8.0156 | 82 | 50 |
7 | 20 | 0.1276 | 0.9918 | 0.1287 | 7.7704 | 1.0082 | 7.8344 | 82 | 40 |
7 | 30 | 0.1305 | 0.9914 | 0.1317 | 7.5958 | 1.0086 | 7.6613 | 82 | 30 |
7 | 40 | 0.1334 | 0.9911 | 0.1346 | 7.4287 | 1.0090 | 7.4957 | 82 | 20 |
7 | 50 | 0.1363 | 0.9907 | 0.1376 | 7.2687 | 1.0094 | 7.3372 | 82 | 10 |
8 | 00 | 0.1392 | 0.9903 | 0.1405 | 7.1154 | 1.0098 | 7.1853 | 82 | 00 |
8 | 10 | 0.1421 | 0.9899 | 0.1435 | 6.9682 | 1.0102 | 7.0396 | 81 | 50 |
8 | 20 | 0.1449 | 0.9894 | 0.1465 | 6.8269 | 1.0107 | 6.8998 | 81 | 40 |
8 | 30 | 0.1478 | 0.9890 | 0.1495 | 6.6912 | 1.0111 | 6.7655 | 81 | 30 |
8 | 40 | 0.1507 | 0.9886 | 0.1524 | 6.5606 | 1.0116 | 6.6363 | 81 | 20 |
8 | 50 | 0.1536 | 0.9881 | 0.1554 | 6.4348 | 1.0120 | 6.5121 | 81 | 10 |
9 | 00 | 0.1564 | 0.9877 | 0.1584 | 6.3138 | 1.0125 | 6.3925 | 81 | 00 |
9 | 10 | 0.1593 | 0.9872 | 0.1614 | 6.1970 | 1.0129 | 6.2772 | 80 | 50 |
9 | 20 | 0.1622 | 0.9868 | 0.1644 | 6.0844 | 1.0134 | 6.1661 | 80 | 40 |
9 | 30 | 0.1650 | 0.9863 | 0.1673 | 5.9758 | 1.0139 | 6.0589 | 80 | 30 |
9 | 40 | 0.1679 | 0.9858 | 0.1703 | 5.8708 | 1.0144 | 5.9554 | 80 | 20 |
9 | 50 | 0.1708 | 0.9853 | 0.1733 | 5.7694 | 1.0149 | 5.8554 | 80 | 10 |
10 | 00 | 0.1736 | 0.9848 | 0.1763 | 5.6713 | 1.0154 | 5.7588 | 80 | 00 |
10 | 10 | 0.1765 | 0.9843 | 0.1793 | 5.5764 | 1.0160 | 5.6653 | 79 | 50 |
10 | 20 | 0.1794 | 0.9838 | 0.1823 | 5.4845 | 1.0165 | 5.5749 | 79 | 40 |
10 | 30 | 0.1822 | 0.9833 | 0.1853 | 5.3955 | 1.0170 | 5.4874 | 79 | 30 |
10 | 40 | 0.1851 | 0.9827 | 0.1883 | 5.3093 | 1.0176 | 5.4026 | 79 | 20 |
10 | 50 | 0.1880 | 0.9822 | 0.1914 | 5.2257 | 1.0181 | 5.3205 | 79 | 10 |
11 | 00 | 0.1908 | 0.9816 | 0.1944 | 5.1446 | 1.0187 | 5.2408 | 79 | 00 |
11 | 10 | 0.1937 | 0.9811 | 0.1974 | 5.0658 | 1.0193 | 5.1636 | 78 | 50 |
11 | 20 | 0.1965 | 0.9805 | 0.2004 | 4.9894 | 1.0199 | 5.0886 | 78 | 40 |
11 | 30 | 0.1994 | 0.9799 | 0.2035 | 4.9152 | 1.0205 | 5.0159 | 78 | 30 |
11 | 40 | 0.2022 | 0.9793 | 0.2065 | 4.8430 | 1.0211 | 4.9452 | 78 | 20 |
11 | 50 | 0.2051 | 0.9787 | 0.2095 | 4.7729 | 1.0217 | 4.8765 | 78 | 10 |
12 | 00 | 0.2079 | 0.9781 | 0.2126 | 4.7046 | 1.0223 | 4.8097 | 78 | 00 |
12 | 10 | 0.2108 | 0.9775 | 0.2156 | 4.6382 | 1.0230 | 4.7448 | 77 | 50 |
12 | 20 | 0.2136 | 0.9769 | 0.2186 | 4.5736 | 1.0236 | 4.6817 | 77 | 40 |
12 | 30 | 0.2164 | 0.9763 | 0.2217 | 4.5107 | 1.0243 | 4.6202 | 77 | 30 |
12 | 40 | 0.2193 | 0.9757 | 0.2247 | 4.4494 | 1.0249 | 4.5604 | 77 | 20 |
12 | 50 | 0.2221 | 0.9750 | 0.2278 | 4.3897 | 1.0256 | 4.5022 | 77 | 10 |
13 | 00 | 0.2250 | 0.9744 | 0.2309 | 4.3315 | 1.0263 | 4.4454 | 77 | 00 |
13 | 10 | 0.2278 | 0.9737 | 0.2339 | 4.2747 | 1.0270 | 4.3901 | 76 | 50 |
13 | 20 | 0.2306 | 0.9730 | 0.2370 | 4.2193 | 1.0277 | 4.3362 | 76 | 40 |
13 | 30 | 0.2334 | 0.9724 | 0.2401 | 4.1653 | 1.0284 | 4.2837 | 76 | 30 |
13 | 40 | 0.2363 | 0.9717 | 0.2432 | 4.1126 | 1.0291 | 4.2324 | 76 | 20 |
13 | 50 | 0.2391 | 0.9710 | 0.2462 | 4.0611 | 1.0299 | 4.1824 | 76 | 10 |
14 | 00 | 0.2419 | 0.9703 | 0.2493 | 4.0108 | 1.0306 | 4.1336 | 76 | 00 |
14 | 10 | 0.2447 | 0.9696 | 0.2524 | 3.9617 | 1.0314 | 4.0859 | 75 | 50 |
14 | 20 | 0.2476 | 0.9689 | 0.2555 | 3.9136 | 1.0321 | 4.0394 | 75 | 40 |
14 | 30 | 0.2504 | 0.9681 | 0.2586 | 3.8667 | 1.0329 | 3.9939 | 75 | 30 |
14 | 40 | 0.2532 | 0.9674 | 0.2617 | 3.8208 | 1.0337 | 3.9495 | 75 | 20 |
14 | 50 | 0.2560 | 0.9667 | 0.2648 | 3.7760 | 1.0345 | 3.9061 | 75 | 10 |
15 | 00 | 0.2588 | 0.9659 | 0.2679 | 3.7321 | 1.0353 | 3.8637 | 75 | 00 |
15 | 10 | 0.2616 | 0.9652 | 0.2711 | 3.6891 | 1.0361 | 3.8222 | 74 | 50 |
15 | 20 | 0.2644 | 0.9644 | 0.2742 | 3.6470 | 1.0369 | 3.7817 | 74 | 40 |
15 | 30 | 0.2672 | 0.9636 | 0.2773 | 3.6059 | 1.0377 | 3.7420 | 74 | 30 |
15 | 40 | 0.2700 | 0.9628 | 0.2805 | 3.5656 | 1.0386 | 3.7032 | 74 | 20 |
15 | 50 | 0.2728 | 0.9621 | 0.2836 | 3.5261 | 1.0394 | 3.6652 | 74 | 10 |
16 | 00 | 0.2756 | 0.9613 | 0.2867 | 3.4874 | 1.0403 | 3.6280 | 74 | 00 |
16 | 10 | 0.2784 | 0.9605 | 0.2899 | 3.4495 | 1.0412 | 3.5915 | 73 | 50 |
16 | 20 | 0.2812 | 0.9596 | 0.2931 | 3.4124 | 1.0421 | 3.5559 | 73 | 40 |
16 | 30 | 0.2840 | 0.9588 | 0.2962 | 3.3759 | 1.0429 | 3.5209 | 73 | 30 |
16 | 40 | 0.2868 | 0.9580 | 0.2994 | 3.3402 | 1.0439 | 3.4867 | 73 | 20 |
16 | 50 | 0.2896 | 0.9572 | 0.3026 | 3.3052 | 1.0448 | 3.4532 | 73 | 10 |
17 | 00 | 0.2924 | 0.9563 | 0.3057 | 3.2709 | 1.0457 | 3.4203 | 73 | 00 |
17 | 10 | 0.2952 | 0.9555 | 0.3089 | 3.2371 | 1.0466 | 3.3881 | 72 | 50 |
17 | 20 | 0.2979 | 0.9546 | 0.3121 | 3.2041 | 1.0476 | 3.3565 | 72 | 40 |
17 | 30 | 0.3007 | 0.9537 | 0.3153 | 3.1716 | 1.0485 | 3.3255 | 72 | 30 |
17 | 40 | 0.3035 | 0.9528 | 0.3185 | 3.1397 | 1.0495 | 3.2951 | 72 | 20 |
17 | 50 | 0.3062 | 0.9520 | 0.3217 | 3.1084 | 1.0505 | 3.2653 | 72 | 10 |
18 | 00 | 0.3090 | 0.9511 | 0.3249 | 3.0777 | 1.0515 | 3.2361 | 72 | 00 |
18 | 10 | 0.3118 | 0.9502 | 0.3281 | 3.0475 | 1.0525 | 3.2074 | 71 | 50 |
18 | 20 | 0.3145 | 0.9492 | 0.3314 | 3.0178 | 1.0535 | 3.1792 | 71 | 40 |
18 | 30 | 0.3173 | 0.9483 | 0.3346 | 2.9887 | 1.0545 | 3.1515 | 71 | 30 |
18 | 40 | 0.3201 | 0.9474 | 0.3378 | 2.9600 | 1.0555 | 3.1244 | 71 | 20 |
18 | 50 | 0.3228 | 0.9465 | 0.3411 | 2.9319 | 1.0566 | 3.0977 | 71 | 10 |
19 | 00 | 0.3256 | 0.9455 | 0.3443 | 2.9042 | 1.0576 | 3.0716 | 71 | 00 |
19 | 10 | 0.3283 | 0.9446 | 0.3476 | 2.8770 | 1.0587 | 3.0458 | 70 | 50 |
19 | 20 | 0.3311 | 0.9436 | 0.3508 | 2.8502 | 1.0598 | 3.0206 | 70 | 40 |
19 | 30 | 0.3338 | 0.9426 | 0.3541 | 2.8239 | 1.0608 | 2.9957 | 70 | 30 |
19 | 40 | 0.3365 | 0.9417 | 0.3574 | 2.7980 | 1.0619 | 2.9713 | 70 | 20 |
19 | 50 | 0.3393 | 0.9407 | 0.3607 | 2.7725 | 1.0631 | 2.9474 | 70 | 10 |
20 | 00 | 0.3420 | 0.9397 | 0.3640 | 2.7475 | 1.0642 | 2.9238 | 70 | 00 |
20 | 10 | 0.3448 | 0.9387 | 0.3673 | 2.7228 | 1.0653 | 2.9006 | 69 | 50 |
20 | 20 | 0.3475 | 0.9377 | 0.3706 | 2.6985 | 1.0665 | 2.8779 | 69 | 40 |
20 | 30 | 0.3502 | 0.9367 | 0.3739 | 2.6746 | 1.0676 | 2.8555 | 69 | 30 |
20 | 40 | 0.3529 | 0.9356 | 0.3772 | 2.6511 | 1.0688 | 2.8334 | 69 | 20 |
20 | 50 | 0.3557 | 0.9346 | 0.3805 | 2.6279 | 1.0700 | 2.8117 | 69 | 10 |
21 | 00 | 0.3584 | 0.9336 | 0.3839 | 2.6051 | 1.0711 | 2.7904 | 69 | 00 |
21 | 10 | 0.3611 | 0.9325 | 0.3872 | 2.5826 | 1.0723 | 2.7695 | 68 | 50 |
21 | 20 | 0.3638 | 0.9315 | 0.3906 | 2.5605 | 1.0736 | 2.7488 | 68 | 40 |
21 | 30 | 0.3665 | 0.9304 | 0.3939 | 2.5386 | 1.0748 | 2.7285 | 68 | 30 |
21 | 40 | 0.3692 | 0.9293 | 0.3973 | 2.5172 | 1.0760 | 2.7085 | 68 | 20 |
21 | 50 | 0.3719 | 0.9283 | 0.4006 | 2.4960 | 1.0773 | 2.6888 | 68 | 10 |
22 | 00 | 0.3746 | 0.9272 | 0.4040 | 2.4751 | 1.0785 | 2.6695 | 68 | 00 |
22 | 10 | 0.3773 | 0.9261 | 0.4074 | 2.4545 | 1.0798 | 2.6504 | 67 | 50 |
22 | 20 | 0.3800 | 0.9250 | 0.4108 | 2.4342 | 1.0811 | 2.6316 | 67 | 40 |
22 | 30 | 0.3827 | 0.9239 | 0.4142 | 2.4142 | 1.0824 | 2.6131 | 67 | 30 |
22 | 40 | 0.3854 | 0.9228 | 0.4176 | 2.3945 | 1.0837 | 2.5949 | 67 | 20 |
22 | 50 | 0.3881 | 0.9216 | 0.4210 | 2.3750 | 1.0850 | 2.5770 | 67 | 10 |
23 | 00 | 0.3907 | 0.9205 | 0.4245 | 2.3559 | 1.0864 | 2.5593 | 67 | 00 |
23 | 10 | 0.3934 | 0.9194 | 0.4279 | 2.3369 | 1.0877 | 2.5419 | 66 | 50 |
23 | 20 | 0.3961 | 0.9182 | 0.4314 | 2.3183 | 1.0891 | 2.5247 | 66 | 40 |
23 | 30 | 0.3987 | 0.9171 | 0.4348 | 2.2998 | 1.0904 | 2.5078 | 66 | 30 |
23 | 40 | 0.4014 | 0.9159 | 0.4383 | 2.2817 | 1.0918 | 2.4912 | 66 | 20 |
23 | 50 | 0.4041 | 0.9147 | 0.4417 | 2.2637 | 1.0932 | 2.4748 | 66 | 10 |
24 | 00 | 0.4067 | 0.9135 | 0.4452 | 2.2460 | 1.0946 | 2.4586 | 66 | 00 |
24 | 10 | 0.4094 | 0.9124 | 0.4487 | 2.2286 | 1.0961 | 2.4426 | 65 | 50 |
24 | 20 | 0.4120 | 0.9112 | 0.4522 | 2.2113 | 1.0975 | 2.4269 | 65 | 40 |
24 | 30 | 0.4147 | 0.9100 | 0.4557 | 2.1943 | 1.0989 | 2.4114 | 65 | 30 |
24 | 40 | 0.4173 | 0.9088 | 0.4592 | 2.1775 | 1.1004 | 2.3961 | 65 | 20 |
24 | 50 | 0.4200 | 0.9075 | 0.4628 | 2.1609 | 1.1019 | 2.3811 | 65 | 10 |
25 | 00 | 0.4226 | 0.9063 | 0.4663 | 2.1445 | 1.1034 | 2.3662 | 65 | 00 |
25 | 10 | 0.4253 | 0.9051 | 0.4699 | 2.1283 | 1.1049 | 2.3515 | 64 | 50 |
25 | 20 | 0.4279 | 0.9038 | 0.4734 | 2.1123 | 1.1064 | 2.3371 | 64 | 40 |
25 | 30 | 0.4305 | 0.9026 | 0.4770 | 2.0965 | 1.1079 | 2.3228 | 64 | 30 |
25 | 40 | 0.4331 | 0.9013 | 0.4806 | 2.0809 | 1.1095 | 2.3088 | 64 | 20 |
25 | 50 | 0.4358 | 0.9001 | 0.4841 | 2.0655 | 1.1110 | 2.2949 | 64 | 10 |
26 | 00 | 0.4384 | 0.8988 | 0.4877 | 2.0503 | 1.1126 | 2.2812 | 64 | 00 |
26 | 10 | 0.4410 | 0.8975 | 0.4913 | 2.0353 | 1.1142 | 2.2677 | 63 | 50 |
26 | 20 | 0.4436 | 0.8962 | 0.4950 | 2.0204 | 1.1158 | 2.2543 | 63 | 40 |
26 | 30 | 0.4462 | 0.8949 | 0.4986 | 2.0057 | 1.1174 | 2.2412 | 63 | 30 |
26 | 40 | 0.4488 | 0.8936 | 0.5022 | 1.9912 | 1.1190 | 2.2282 | 63 | 20 |
26 | 50 | 0.4514 | 0.8923 | 0.5059 | 1.9768 | 1.1207 | 2.2153 | 63 | 10 |
27 | 00 | 0.4540 | 0.8910 | 0.5095 | 1.9626 | 1.1223 | 2.2027 | 63 | 00 |
27 | 10 | 0.4566 | 0.8897 | 0.5132 | 1.9486 | 1.1240 | 2.1902 | 62 | 50 |
27 | 20 | 0.4592 | 0.8884 | 0.5169 | 1.9347 | 1.1257 | 2.1779 | 62 | 40 |
27 | 30 | 0.4617 | 0.8870 | 0.5206 | 1.9210 | 1.1274 | 2.1657 | 62 | 30 |
27 | 40 | 0.4643 | 0.8857 | 0.5243 | 1.9074 | 1.1291 | 2.1537 | 62 | 20 |
27 | 50 | 0.4669 | 0.8843 | 0.5280 | 1.8940 | 1.1308 | 2.1418 | 62 | 10 |
28 | 00 | 0.4695 | 0.8829 | 0.5317 | 1.8807 | 1.1326 | 2.1301 | 62 | 00 |
28 | 10 | 0.4720 | 0.8816 | 0.5354 | 1.8676 | 1.1343 | 2.1185 | 61 | 50 |
28 | 20 | 0.4746 | 0.8802 | 0.5392 | 1.8546 | 1.1361 | 2.1070 | 61 | 40 |
28 | 30 | 0.4772 | 0.8788 | 0.5430 | 1.8418 | 1.1379 | 2.0957 | 61 | 30 |
28 | 40 | 0.4797 | 0.8774 | 0.5467 | 1.8291 | 1.1397 | 2.0846 | 61 | 20 |
28 | 50 | 0.4823 | 0.8760 | 0.5505 | 1.8165 | 1.1415 | 2.0736 | 61 | 10 |
29 | 00 | 0.4848 | 0.8746 | 0.5543 | 1.8040 | 1.1434 | 2.0627 | 61 | 00 |
29 | 10 | 0.4874 | 0.8732 | 0.5581 | 1.7917 | 1.1452 | 2.0519 | 60 | 50 |
29 | 20 | 0.4899 | 0.8718 | 0.5619 | 1.7796 | 1.1471 | 2.0413 | 60 | 40 |
29 | 30 | 0.4924 | 0.8704 | 0.5658 | 1.7675 | 1.1490 | 2.0308 | 60 | 30 |
29 | 40 | 0.4950 | 0.8689 | 0.5696 | 1.7556 | 1.1509 | 2.0204 | 60 | 20 |
29 | 50 | 0.4975 | 0.8675 | 0.5735 | 1.7437 | 1.1528 | 2.0101 | 60 | 10 |
30 | 00 | 0.5000 | 0.8660 | 0.5774 | 1.7321 | 1.1547 | 2.0000 | 60 | 00 |
30 | 10 | 0.5025 | 0.8646 | 0.5812 | 1.7205 | 1.1566 | 1.9900 | 59 | 50 |
30 | 20 | 0.5050 | 0.8631 | 0.5851 | 1.7090 | 1.1586 | 1.9801 | 59 | 40 |
30 | 30 | 0.5075 | 0.8616 | 0.5890 | 1.6977 | 1.1606 | 1.9703 | 59 | 30 |
30 | 40 | 0.5100 | 0.8601 | 0.5930 | 1.6864 | 1.1626 | 1.9606 | 59 | 20 |
30 | 50 | 0.5125 | 0.8587 | 0.5969 | 1.6753 | 1.1646 | 1.9511 | 59 | 10 |
31 | 00 | 0.5150 | 0.8572 | 0.6009 | 1.6643 | 1.1666 | 1.9416 | 59 | 00 |
31 | 10 | 0.5175 | 0.8557 | 0.6048 | 1.6534 | 1.1687 | 1.9323 | 58 | 50 |
31 | 20 | 0.5200 | 0.8542 | 0.6088 | 1.6426 | 1.1707 | 1.9230 | 58 | 40 |
31 | 30 | 0.5225 | 0.8526 | 0.6128 | 1.6319 | 1.1728 | 1.9139 | 58 | 30 |
31 | 40 | 0.5250 | 0.8511 | 0.6168 | 1.6212 | 1.1749 | 1.9048 | 58 | 20 |
31 | 50 | 0.5275 | 0.8496 | 0.6208 | 1.6107 | 1.1770 | 1.8959 | 58 | 10 |
32 | 00 | 0.5299 | 0.8480 | 0.6249 | 1.6003 | 1.1792 | 1.8871 | 58 | 00 |
32 | 10 | 0.5324 | 0.8465 | 0.6289 | 1.5900 | 1.1813 | 1.8783 | 57 | 50 |
32 | 20 | 0.5348 | 0.8450 | 0.6330 | 1.5798 | 1.1835 | 1.8697 | 57 | 40 |
32 | 30 | 0.5373 | 0.8434 | 0.6371 | 1.5697 | 1.1857 | 1.8612 | 57 | 30 |
32 | 40 | 0.5398 | 0.8418 | 0.6412 | 1.5597 | 1.1879 | 1.8527 | 57 | 20 |
32 | 50 | 0.5422 | 0.8403 | 0.6453 | 1.5497 | 1.1901 | 1.8443 | 57 | 10 |
33 | 00 | 0.5446 | 0.8387 | 0.6494 | 1.5399 | 1.1924 | 1.8361 | 57 | 00 |
33 | 10 | 0.5471 | 0.8371 | 0.6536 | 1.5301 | 1.1946 | 1.8279 | 56 | 50 |
33 | 20 | 0.5495 | 0.8355 | 0.6577 | 1.5204 | 1.1969 | 1.8198 | 56 | 40 |
33 | 30 | 0.5519 | 0.8339 | 0.6619 | 1.5108 | 1.1992 | 1.8118 | 56 | 30 |
33 | 40 | 0.5544 | 0.8323 | 0.6661 | 1.5013 | 1.2015 | 1.8039 | 56 | 20 |
33 | 50 | 0.5568 | 0.8307 | 0.6703 | 1.4919 | 1.2039 | 1.7960 | 56 | 10 |
34 | 00 | 0.5592 | 0.8290 | 0.6745 | 1.4826 | 1.2062 | 1.7883 | 56 | 00 |
34 | 10 | 0.5616 | 0.8274 | 0.6787 | 1.4733 | 1.2086 | 1.7806 | 55 | 50 |
34 | 20 | 0.5640 | 0.8258 | 0.6830 | 1.4641 | 1.2110 | 1.7730 | 55 | 40 |
34 | 30 | 0.5664 | 0.8241 | 0.6873 | 1.4550 | 1.2134 | 1.7655 | 55 | 30 |
34 | 40 | 0.5688 | 0.8225 | 0.6916 | 1.4460 | 1.2158 | 1.7581 | 55 | 20 |
34 | 50 | 0.5712 | 0.8208 | 0.6959 | 1.4370 | 1.2183 | 1.7507 | 55 | 10 |
35 | 00 | 0.5736 | 0.8192 | 0.7002 | 1.4281 | 1.2208 | 1.7434 | 55 | 00 |
35 | 10 | 0.5760 | 0.8175 | 0.7046 | 1.4193 | 1.2233 | 1.7362 | 54 | 50 |
35 | 20 | 0.5783 | 0.8158 | 0.7089 | 1.4106 | 1.2258 | 1.7291 | 54 | 40 |
35 | 30 | 0.5807 | 0.8141 | 0.7133 | 1.4019 | 1.2283 | 1.7221 | 54 | 30 |
35 | 40 | 0.5831 | 0.8124 | 0.7177 | 1.3934 | 1.2309 | 1.7151 | 54 | 20 |
35 | 50 | 0.5854 | 0.8107 | 0.7221 | 1.3848 | 1.2335 | 1.7081 | 54 | 10 |
36 | 00 | 0.5878 | 0.8090 | 0.7265 | 1.3764 | 1.2361 | 1.7013 | 54 | 00 |
36 | 10 | 0.5901 | 0.8073 | 0.7310 | 1.3680 | 1.2387 | 1.6945 | 53 | 50 |
36 | 20 | 0.5925 | 0.8056 | 0.7355 | 1.3597 | 1.2413 | 1.6878 | 53 | 40 |
36 | 30 | 0.5948 | 0.8039 | 0.7400 | 1.3514 | 1.2440 | 1.6812 | 53 | 30 |
36 | 40 | 0.5972 | 0.8021 | 0.7445 | 1.3432 | 1.2467 | 1.6746 | 53 | 20 |
36 | 50 | 0.5995 | 0.8004 | 0.7490 | 1.3351 | 1.2494 | 1.6681 | 53 | 10 |
37 | 00 | 0.6018 | 0.7986 | 0.7536 | 1.3270 | 1.2521 | 1.6616 | 53 | 00 |
37 | 10 | 0.6041 | 0.7969 | 0.7581 | 1.3190 | 1.2549 | 1.6553 | 52 | 50 |
37 | 20 | 0.6065 | 0.7951 | 0.7627 | 1.3111 | 1.2577 | 1.6489 | 52 | 40 |
37 | 30 | 0.6088 | 0.7934 | 0.7673 | 1.3032 | 1.2605 | 1.6427 | 52 | 30 |
37 | 40 | 0.6111 | 0.7916 | 0.7720 | 1.2954 | 1.2633 | 1.6365 | 52 | 20 |
37 | 50 | 0.6134 | 0.7898 | 0.7766 | 1.2876 | 1.2661 | 1.6303 | 52 | 10 |
38 | 00 | 0.6157 | 0.7880 | 0.7813 | 1.2799 | 1.2690 | 1.6243 | 52 | 00 |
38 | 10 | 0.6180 | 0.7862 | 0.7860 | 1.2723 | 1.2719 | 1.6183 | 51 | 50 |
38 | 20 | 0.6202 | 0.7844 | 0.7907 | 1.2647 | 1.2748 | 1.6123 | 51 | 40 |
38 | 30 | 0.6225 | 0.7826 | 0.7954 | 1.2572 | 1.2778 | 1.6064 | 51 | 30 |
38 | 40 | 0.6248 | 0.7808 | 0.8002 | 1.2497 | 1.2807 | 1.6005 | 51 | 20 |
38 | 50 | 0.6271 | 0.7790 | 0.8050 | 1.2423 | 1.2837 | 1.5948 | 51 | 10 |
39 | 00 | 0.6293 | 0.7771 | 0.8098 | 1.2349 | 1.2868 | 1.5890 | 51 | 00 |
39 | 10 | 0.6316 | 0.7753 | 0.8146 | 1.2276 | 1.2898 | 1.5833 | 50 | 50 |
39 | 20 | 0.6338 | 0.7735 | 0.8195 | 1.2203 | 1.2929 | 1.5777 | 50 | 40 |
39 | 30 | 0.6361 | 0.7716 | 0.8243 | 1.2131 | 1.2960 | 1.5721 | 50 | 30 |
39 | 40 | 0.6383 | 0.7698 | 0.8292 | 1.2059 | 1.2991 | 1.5666 | 50 | 20 |
39 | 50 | 0.6406 | 0.7679 | 0.8342 | 1.1988 | 1.3022 | 1.5611 | 50 | 10 |
40 | 00 | 0.6428 | 0.7660 | 0.8391 | 1.1918 | 1.3054 | 1.5557 | 50 | 00 |
40 | 10 | 0.6450 | 0.7642 | 0.8441 | 1.1847 | 1.3086 | 1.5504 | 49 | 50 |
40 | 20 | 0.6472 | 0.7623 | 0.8491 | 1.1778 | 1.3118 | 1.5450 | 49 | 40 |
40 | 30 | 0.6494 | 0.7604 | 0.8541 | 1.1708 | 1.3151 | 1.5398 | 49 | 30 |
40 | 40 | 0.6517 | 0.7585 | 0.8591 | 1.1640 | 1.3184 | 1.5345 | 49 | 20 |
40 | 50 | 0.6539 | 0.7566 | 0.8642 | 1.1571 | 1.3217 | 1.5294 | 49 | 10 |
41 | 00 | 0.6561 | 0.7547 | 0.8693 | 1.1504 | 1.3250 | 1.5243 | 49 | 00 |
41 | 10 | 0.6583 | 0.7528 | 0.8744 | 1.1436 | 1.3284 | 1.5192 | 48 | 50 |
41 | 20 | 0.6604 | 0.7509 | 0.8796 | 1.1369 | 1.3318 | 1.5141 | 48 | 40 |
41 | 30 | 0.6626 | 0.7490 | 0.8847 | 1.1303 | 1.3352 | 1.5092 | 48 | 30 |
41 | 40 | 0.6648 | 0.7470 | 0.8899 | 1.1237 | 1.3386 | 1.5042 | 48 | 20 |
41 | 50 | 0.6670 | 0.7451 | 0.8952 | 1.1171 | 1.3421 | 1.4993 | 48 | 10 |
42 | 00 | 0.6691 | 0.7431 | 0.9004 | 1.1106 | 1.3456 | 1.4945 | 48 | 00 |
42 | 10 | 0.6713 | 0.7412 | 0.9057 | 1.1041 | 1.3492 | 1.4897 | 47 | 50 |
42 | 20 | 0.6734 | 0.7392 | 0.9110 | 1.0977 | 1.3527 | 1.4849 | 47 | 40 |
42 | 30 | 0.6756 | 0.7373 | 0.9163 | 1.0913 | 1.3563 | 1.4802 | 47 | 30 |
42 | 40 | 0.6777 | 0.7353 | 0.9217 | 1.0850 | 1.3600 | 1.4755 | 47 | 20 |
42 | 50 | 0.6799 | 0.7333 | 0.9271 | 1.0786 | 1.3636 | 1.4709 | 47 | 10 |
43 | 00 | 0.6820 | 0.7314 | 0.9325 | 1.0724 | 1.3673 | 1.4663 | 47 | 00 |
43 | 10 | 0.6841 | 0.7294 | 0.9380 | 1.0661 | 1.3711 | 1.4617 | 46 | 50 |
43 | 20 | 0.6862 | 0.7274 | 0.9435 | 1.0599 | 1.3748 | 1.4572 | 46 | 40 |
43 | 30 | 0.6884 | 0.7254 | 0.9490 | 1.0538 | 1.3786 | 1.4527 | 46 | 30 |
43 | 40 | 0.6905 | 0.7234 | 0.9545 | 1.0477 | 1.3824 | 1.4483 | 46 | 20 |
43 | 50 | 0.6926 | 0.7214 | 0.9601 | 1.0416 | 1.3863 | 1.4439 | 46 | 10 |
44 | 00 | 0.6947 | 0.7193 | 0.9657 | 1.0355 | 1.3902 | 1.4396 | 46 | 00 |
44 | 10 | 0.6967 | 0.7173 | 0.9713 | 1.0295 | 1.3941 | 1.4352 | 45 | 50 |
44 | 20 | 0.6988 | 0.7153 | 0.9770 | 1.0235 | 1.3980 | 1.4310 | 45 | 40 |
44 | 30 | 0.7009 | 0.7133 | 0.9827 | 1.0176 | 1.4020 | 1.4267 | 45 | 30 |
44 | 40 | 0.7030 | 0.7112 | 0.9884 | 1.0117 | 1.4061 | 1.4225 | 45 | 20 |
44 | 50 | 0.7050 | 0.7092 | 0.9942 | 1.0058 | 1.4101 | 1.4183 | 45 | 10 |
45 | 00 | 0.7071 | 0.7071 | 1.0000 | 1.0000 | 1.4142 | 1.4142 | 45 | 00 |
度 | 分 | cos | sin | cot | tan | csc | sec | 度 | 分 |