三角函數

三角函數的基本定義

${\displaystyle \sin x={\frac {a}{c}}={\frac {\text{對 邊 長 }}{\text{斜 邊 長 }}}}$

${\displaystyle \cos x={\frac {b}{c}}={\frac {\text{鄰 邊 長 }}{\text{斜 邊 長 }}}}$

${\displaystyle \tan x={\frac {a}{b}}={\frac {\text{對 邊 長 }}{\text{鄰 邊 長 }}}}$

${\displaystyle 270^{\circ }<\phi \leq 360^{\circ }}$時，${\displaystyle -1<\sin \phi \leq 0}$${\displaystyle 0<\cos \phi \leq 1}$

弧度制與角度制的轉換

${\displaystyle {rad}=\pi {\frac {deg}{180^{\circ }}}}$

${\displaystyle 2\pi \leftrightarrow 360^{\circ }}$
${\displaystyle \pi \leftrightarrow 180^{\circ }}$
${\displaystyle {\frac {\pi }{2}}\leftrightarrow 90^{\circ }}$
${\displaystyle {\frac {\pi }{3}}\leftrightarrow 60^{\circ }}$
${\displaystyle {\frac {\pi }{4}}\leftrightarrow 45^{\circ }}$
${\displaystyle {\frac {\pi }{6}}\leftrightarrow 30^{\circ }}$

主要的公式

倒數關係

${\displaystyle \sin \alpha ={\frac {1}{\csc \alpha }}}$

${\displaystyle \cos \beta ={\frac {1}{\sec \beta }}}$

${\displaystyle \tan \theta ={\frac {1}{\cot \theta }}}$

平方相加

${\displaystyle \cos ^{2}\theta +\sin ^{2}\theta =1}$
${\displaystyle \tan ^{2}\theta +1=\sec ^{2}\theta }$
${\displaystyle 1+\cot ^{2}\theta =\csc ^{2}\theta }$

和角公式

${\displaystyle \sin(\alpha \pm \beta )=\sin \alpha \cos \beta \pm \cos \alpha \sin \beta }$

${\displaystyle \cos(\alpha \pm \beta )=\cos \alpha \cos \beta \mp \sin \alpha \sin \beta }$

${\displaystyle \tan(\alpha \pm \beta )={\frac {\tan \alpha \pm \tan \beta }{1\mp \tan \alpha \tan \beta }}}$

倍角公式 & 半角公式

2倍角公式:

${\displaystyle \sin 2\theta =2\sin \theta \cos \theta }$

${\displaystyle \cos 2\theta =\cos ^{2}\theta -\sin ^{2}\theta =2\cos ^{2}\theta -1=1-2\sin ^{2}\theta }$

${\displaystyle \tan 2\theta ={\frac {2\tan \theta }{1-\tan ^{2}\theta }}}$

3倍角公式:

${\displaystyle \cos 3\theta =4\cos ^{3}\theta -3\cos \theta }$

${\displaystyle \sin 3\theta =-4\sin ^{3}\theta +3\sin \theta }$

${\displaystyle \sin {\frac {\theta }{2}}=\pm {\sqrt {\frac {1-\cos \theta }{2}}}}$

${\displaystyle \cos {\frac {\theta }{2}}=\pm {\sqrt {\frac {1+\cos \theta }{2}}}}$

${\displaystyle \tan {\frac {\theta }{2}}=\pm {\sqrt {\frac {1-\cos \theta }{1+cos\theta }}}={\frac {\sin \theta }{1+\cos \theta }}={\frac {1-\cos \theta }{\sin \theta }}}$

${\displaystyle \sin \alpha \cos \beta ={\frac {\sin(\alpha +\beta )+\sin(\alpha -\beta )}{2}}}$

${\displaystyle \cos \alpha \sin \beta ={\frac {\sin(\alpha +\beta )-\sin(\alpha -\beta )}{2}}}$

${\displaystyle \cos \alpha \cos \beta ={\frac {\cos(\alpha +\beta )+\cos(\alpha -\beta )}{2}}}$

${\displaystyle \sin \alpha \sin \beta ={\frac {\cos(\alpha -\beta )-\cos(\alpha +\beta )}{2}}}$

${\displaystyle \sin \alpha +\sin \beta =2\sin {\frac {\alpha +\beta }{2}}\cos {\frac {\alpha -\beta }{2}}}$

${\displaystyle \sin \alpha -\sin \beta =2\cos {\frac {\alpha +\beta }{2}}\sin {\frac {\alpha -\beta }{2}}}$

${\displaystyle \cos \alpha +\cos \beta =2\cos {\frac {\alpha +\beta }{2}}\cos {\frac {\alpha -\beta }{2}}}$

${\displaystyle \cos \alpha -\cos \beta =-2\sin {\frac {\alpha +\beta }{2}}\sin {\frac {\alpha -\beta }{2}}}$

其他公式

${\displaystyle \sin 2\alpha ={\frac {2\tan \alpha }{1+\tan ^{2}\alpha }}}$

${\displaystyle \cos 2\alpha ={\frac {1-\tan ^{2}\alpha }{1+\tan ^{2}\alpha }}}$

${\displaystyle \tan 2\alpha ={\frac {2\tan \alpha }{1-\tan ^{2}\alpha }}}$

${\displaystyle \sin(\alpha +\beta )\cdot \sin(\alpha -\beta )=\sin ^{2}\alpha -\sin ^{2}\beta }$

${\displaystyle \cos(\alpha +\beta )\cdot \cos(\alpha -\beta )=\cos ^{2}\alpha -\sin ^{2}\beta }$

${\displaystyle \cos ^{2}\alpha ={\frac {1+\cos 2\alpha }{2}}}$

${\displaystyle \sin ^{2}\alpha ={\frac {1-\cos 2\alpha }{2}}}$

${\displaystyle a\sin \alpha +b\cos \alpha ={\sqrt {a^{2}+b^{2}}}\cdot \sin \left(\alpha +\arctan {\frac {b}{a}}\right)}$

三角分析

${\displaystyle S={\frac {1}{2}}ah={\frac {1}{2}}bc\sin A={\frac {1}{2}}ab\sin C={\frac {1}{2}}ac\sin B={\frac {abc}{4R}}=2R^{2}\sin A\sin B\sin C}$

1) ${\displaystyle c}$為三角形${\displaystyle ABC}$最大邊時

${\displaystyle a^{2}+b^{2}=c^{2}}$三角形${\displaystyle ABC}$為直角三角形

${\displaystyle a^{2}+b^{2}>c^{2}}$三角形${\displaystyle ABC}$為銳角三角形

${\displaystyle a^{2}+b^{2}三角形${\displaystyle ABC}$為鈍角三角形

2) ${\displaystyle A推出 ${\displaystyle \sin A<\sin B}$

附錄表

附錄─三角函數表

 度 分 sin cos tan cot sec csc 度 分 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 度 分 cos sin cot tan csc sec 度 分