"역삼각함수"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) |
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| (사용자 2명의 중간 판 22개는 보이지 않습니다) | |||
| 1번째 줄: | 1번째 줄: | ||
| − | + | ==개요== | |
| − | * | + | * 사인/아크사인함수 덧셈정리의 적분표현:<math>\sin \left(\theta_1+\theta_2\right)=\sin \theta_1 \cos \theta_2 + \cos \theta_1 \sin \theta_2</math>:<math>\arcsin x+\arcsin y=\arcsin (x\sqrt{1-y^2}+y\sqrt{1-x^2})</math>:<math>\int_0^x{\frac{1}{\sqrt{1-x^2}}}dx+\int_0^y{\frac{1}{\sqrt{1-x^2}}}dx = \int_0^{x\sqrt{1-y^2}+y\sqrt{1-x^2}}{\frac{1}{\sqrt{1-x^2}}}dx </math> |
| + | * 탄젠트/아크탄젠트 함수 덧셈정리의 적분표현:<math>\tan(\theta_1+\theta_2)=\frac{\tan\theta_1+\tan\theta_2}{1-\tan\theta_1\tan\theta_2}</math>:<math>\arctan x+\arctan y = \arctan{\frac{x+y}{1-xy}}</math>:<math>\int_0^x \frac{dx}{1+x^2} + \int_0^y \frac{dx}{1+x^2} = \int_0^{\frac{x+y}{1-xy}} \frac{dx}{1+x^2}</math> | ||
| − | + | <math>x>0</math> 일 때, | |
| − | + | <math>\arctan x+\arctan \frac{1}{x} = \frac{\pi}{2}</math> | |
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<math>2(\arcsin x)^2=\sum_{n=1}^{\infty}\frac{(2x)^{2n}}{n^2\binom{2n}{n}}</math> | <math>2(\arcsin x)^2=\sum_{n=1}^{\infty}\frac{(2x)^{2n}}{n^2\binom{2n}{n}}</math> | ||
| 20번째 줄: | 14번째 줄: | ||
<math>\frac{2x \arcsin x}{\sqrt{1-x^2}}=\sum_{n=1}^{\infty}\frac{(2x)^{2n}}{n\binom{2n}{n}}</math> | <math>\frac{2x \arcsin x}{\sqrt{1-x^2}}=\sum_{n=1}^{\infty}\frac{(2x)^{2n}}{n\binom{2n}{n}}</math> | ||
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| − | + | ==역사== | |
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| − | + | * | |
| + | * http://www.google.com/search?hl=en&tbs=tl:1&q=inverse+tangent | ||
| − | + | * http://www.google.com/search?hl=en&tbs=tl:1&q=arctangent http://www.google.com/search?hl=en&tbs=tl:1&q= | |
| + | * [[수학사 연표]] | ||
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| − | + | ==메모== | |
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| − | + | ==관련된 항목들== | |
| − | + | * [[대수적 함수와 아벨적분]] | |
| + | * [[중심이항계수(central binomial coefficient)]] | ||
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| − | + | ==수학용어번역== | |
| − | * [[ | + | * 단어사전 http://www.google.com/dictionary?langpair=en|ko&q= |
| − | * [ | + | * 발음사전 http://www.forvo.com/search/ |
| + | * [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집] | ||
| + | ** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr= | ||
| + | * [http://www.nktech.net/science/term/term_l.jsp?l_mode=cate&s_code_cd=MA 남·북한수학용어비교] | ||
| + | * [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학용어한글화 게시판] | ||
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| − | + | ==매스매티카 파일 및 계산 리소스== | |
| − | * | + | * https://docs.google.com/file/d/0B8XXo8Tve1cxT3d5dGR5X1dIVDQ/edit |
| − | * | + | * http://www.wolframalpha.com/input/?i= |
| − | * | + | * http://functions.wolfram.com/ |
| − | * | + | * [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions] |
| − | * [http://www. | + | * [http://people.math.sfu.ca/%7Ecbm/aands/toc.htm Abramowitz and Stegun Handbook of mathematical functions] |
| − | * [http:// | + | * [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences] |
| + | * [http://numbers.computation.free.fr/Constants/constants.html Numbers, constants and computation] | ||
| + | * [https://docs.google.com/open?id=0B8XXo8Tve1cxMWI0NzNjYWUtNmIwZi00YzhkLTkzNzQtMDMwYmVmYmIxNmIw 매스매티카 파일 목록] | ||
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| − | + | ==사전 형태의 자료== | |
* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
| 80번째 줄: | 82번째 줄: | ||
* http://www.wolframalpha.com/input/?i= | * http://www.wolframalpha.com/input/?i= | ||
* [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions] | * [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions] | ||
| − | * [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences] | + | * [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences] |
** http://www.research.att.com/~njas/sequences/?q= | ** http://www.research.att.com/~njas/sequences/?q= | ||
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| − | + | ==블로그== | |
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| − | + | [[분류:삼각함수]] | |
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2020년 12월 28일 (월) 03:44 기준 최신판
개요
- 사인/아크사인함수 덧셈정리의 적분표현\[\sin \left(\theta_1+\theta_2\right)=\sin \theta_1 \cos \theta_2 + \cos \theta_1 \sin \theta_2\]\[\arcsin x+\arcsin y=\arcsin (x\sqrt{1-y^2}+y\sqrt{1-x^2})\]\[\int_0^x{\frac{1}{\sqrt{1-x^2}}}dx+\int_0^y{\frac{1}{\sqrt{1-x^2}}}dx = \int_0^{x\sqrt{1-y^2}+y\sqrt{1-x^2}}{\frac{1}{\sqrt{1-x^2}}}dx \]
- 탄젠트/아크탄젠트 함수 덧셈정리의 적분표현\[\tan(\theta_1+\theta_2)=\frac{\tan\theta_1+\tan\theta_2}{1-\tan\theta_1\tan\theta_2}\]\[\arctan x+\arctan y = \arctan{\frac{x+y}{1-xy}}\]\[\int_0^x \frac{dx}{1+x^2} + \int_0^y \frac{dx}{1+x^2} = \int_0^{\frac{x+y}{1-xy}} \frac{dx}{1+x^2}\]
\(x>0\) 일 때,
\(\arctan x+\arctan \frac{1}{x} = \frac{\pi}{2}\)
\(2(\arcsin x)^2=\sum_{n=1}^{\infty}\frac{(2x)^{2n}}{n^2\binom{2n}{n}}\)
\(\frac{2x \arcsin x}{\sqrt{1-x^2}}=\sum_{n=1}^{\infty}\frac{(2x)^{2n}}{n\binom{2n}{n}}\)
역사
- http://www.google.com/search?hl=en&tbs=tl:1&q=arctangent http://www.google.com/search?hl=en&tbs=tl:1&q=
- 수학사 연표
메모
관련된 항목들
수학용어번역
- 단어사전 http://www.google.com/dictionary?langpair=en%7Cko&q=
- 발음사전 http://www.forvo.com/search/
- 대한수학회 수학 학술 용어집
- 남·북한수학용어비교
- 대한수학회 수학용어한글화 게시판
매스매티카 파일 및 계산 리소스
- https://docs.google.com/file/d/0B8XXo8Tve1cxT3d5dGR5X1dIVDQ/edit
- http://www.wolframalpha.com/input/?i=
- http://functions.wolfram.com/
- NIST Digital Library of Mathematical Functions
- Abramowitz and Stegun Handbook of mathematical functions
- The On-Line Encyclopedia of Integer Sequences
- Numbers, constants and computation
- 매스매티카 파일 목록
사전 형태의 자료
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- http://www.wolframalpha.com/input/?i=
- NIST Digital Library of Mathematical Functions
- The On-Line Encyclopedia of Integer Sequences