三角函數

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三角函數的基本定義[编辑]

圖一

三角函數最一開始是用來表示角度和直角三角形三邊邊長關係的式子,直角三角形中的可由畢氏定理給出它的定義: 若一個直角三角形,它的一個銳角角度為x,此角的對邊為a,鄰邊為b,斜邊為c(如圖所示),則:

因此得到正弦函數sin x和餘弦函數cos x的定義.

廣義的定義[编辑]

圖二
圖三

三角函數的廣義定義是定義在單位圓(如圖二所示)上的,不管角度為何,廣義的定義皆為其斜邊與X軸的夾角來取其值,且若其斜邊和單位圓的交點為(x,y)(如圖三所示),則:

因此可推出:

時,

時,

時,

時,

弧度制與角度制的轉換[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:

積化和差:

和差化積:

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:

三角函數的一些進階定理[编辑]

正弦定理:

若為任意三角形的三邊,A,B,C分別為a,b,c的對角,R為此三角形的外接圓半徑,則存有以下關係式:

由勾股定理得 当θ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θ≠kπ+(k∈z)时,有

这就是说,同一个角θ的正弦、余弦的平方和等于1,商等于角θ的正切。

三角分析[编辑]

面积公式:

三角形形状的判定:

1) c为三角形ABC最大边时

三角形ABC为直角三角形

三角形ABC为锐角三角形

三角形ABC为钝角三角形

2) A<B 推出

三角函數應用[编辑]

三角測量[编辑]

其他應用[编辑]

習題[编辑]

附錄─三角函數表[编辑]

sin cos tan cot sec csc
0 00 0.0000 1.0000 0.0000 未定義 1.0000 未定義 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
cos sin cot tan csc sec