អនុគមន៍កូស៊ីនុសជាប្រភេទមួយនៃអនុគមន៍ត្រីកោណមាត្រគ្រឹះ។ តំលៃនៃអនុគមន៍កូស៊ីនុសក្នុងដែនកំនត់ពិតគឺស្ថិតនៅចន្លោះ
។ វាជាអនុគមន៍ខួបដែលមានខួបស្មើ
។
កូស៊ីនុសនៃមុំមួយ
គឺជាផលធៀបរវាងរង្វាស់ប្រវែងនៃជ្រុងជាប់ និង រង្វាស់អ៊ីប៉ូតេនុស។
យើងតាង
- អ៊ីប៉ូតេនុស (AC) ដោយ
![{\displaystyle \ h}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8eb515077d0b969895a7e62dfe0ae6a198e2426f)
- ជ្រុងជាប់ (AB) ដោយ
នៃមុំ
។
យើងបាន
![{\displaystyle \sin \theta ={\frac {AB}{AC}}={\frac {c}{h}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a73998d660d12289509a1a70fb48e9a11ce58eff)
អនុគមន៍
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sin
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cos
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tan
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csc
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sec
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cot
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- រូបមន្តកូស៊ីនុសនៃផលបូកនិងផលដករវាងមុំពីរ
![{\displaystyle \cos \left(x+y\right)=\cos x\cos y-\sin x\sin y}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4d6c1f8820258d3db350d332f76ccd8b12a3900c)
![{\displaystyle \cos \left(x-y\right)=\cos x\cos y+\sin x\sin y}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8ef8ff180ff764621c697ccbce00d1f9042abf8b)
![{\displaystyle \cos(2\theta )=\cos ^{2}\theta -\sin ^{2}\theta \,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e98ef33f32a94b7d126c99f14a602552fcb172e7)
![{\displaystyle \cos 3\theta =4\cos ^{3}\theta -3\cos \theta \,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e005910f2963beb3ad6ee3831c244398b0c7d24f)
![{\displaystyle \cos {\frac {\theta }{2}}=\pm \,{\sqrt {\frac {1+\cos \theta }{2}}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/14ff0371f6222093daf9699f3302eb3f19816d1b)
- រូបមន្តផលបូកនិងផលដកកូស៊ីនុស
![{\displaystyle \cos \theta +\cos \phi =2\cos \left({\frac {\theta +\phi }{2}}\right)\cos \left({\frac {\theta -\phi }{2}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1e09155004c19d563a2e6efc448e8a23ca66f63c)
![{\displaystyle \cos \theta -\cos \phi =-2\sin \left({\theta +\phi \over 2}\right)\sin \left({\theta -\phi \over 2}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7cf22db61db2932f000e496dfd3a6f969f83d402)
- ទំនាក់ទំនងរវាងកូស៊ីនុសនិងតង់សង់កន្លះមុំ
![{\displaystyle \cos \alpha ={\frac {1-\tan ^{2}{\frac {\alpha }{2}}}{1+\tan ^{2}{\frac {\alpha }{2}}}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7441fbdc780dc96e498160cfbda4ace7eabb5ab0)
អាំងតេក្រាលដែលមានកូស៊ីនុស
[កែប្រែ]
![{\displaystyle \int \cos cx\;dx={\frac {1}{c}}\sin cx\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cd5a071bc63ba7f827d559d720b4e5ef34b64d48)
![{\displaystyle \int \cos ^{n}cx\;dx={\frac {\cos ^{n-1}cx\sin cx}{nc}}+{\frac {n-1}{n}}\int \cos ^{n-2}cx\;dx\qquad {\mbox{(}}n>0{\mbox{)}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/970d60b0e87421f02cfaa5672e6ce8a23aece7f7)
![{\displaystyle \int x\cos cx\;dx={\frac {\cos cx}{c^{2}}}+{\frac {x\sin cx}{c}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7c5fc103923703bd335b87b1bffc18e6ed72832e)
![{\displaystyle \int x^{n}\cos cx\;dx={\frac {x^{n}\sin cx}{c}}-{\frac {n}{c}}\int x^{n-1}\sin cx\;dx\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/593a0631f1f6c5d29a40eed7e6035a515ff8e3d6)
![{\displaystyle \int _{\frac {-a}{2}}^{\frac {a}{2}}x^{2}\cos ^{2}{\frac {n\pi x}{a}}\;dx={\frac {a^{3}(n^{2}\pi ^{2}-6)}{24n^{2}\pi ^{2}}}\qquad {\mbox{(}}n=1,3,5...{\mbox{)}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6daaf46dda633fcab2732530494a5d13379811d9)
![{\displaystyle \int {\frac {\cos cx}{x}}dx=\ln |cx|+\sum _{i=1}^{\infty }(-1)^{i}{\frac {(cx)^{2i}}{2i\cdot (2i)!}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/babee406174e7983169482bebe8d2f7b8f05a2f6)
![{\displaystyle \int {\frac {\cos cx}{x^{n}}}dx=-{\frac {\cos cx}{(n-1)x^{n-1}}}-{\frac {c}{n-1}}\int {\frac {\sin cx}{x^{n-1}}}dx\qquad {\mbox{(}}n\neq 1{\mbox{)}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3a003beb101a0d8ff3efbffc7d465d3841654472)
![{\displaystyle \int {\frac {dx}{\cos cx}}={\frac {1}{c}}\ln \left|\tan \left({\frac {cx}{2}}+{\frac {\pi }{4}}\right)\right|}](https://wikimedia.org/api/rest_v1/media/math/render/svg/136d5e28887252d271d77638ae7c15b2b32c09f6)
![{\displaystyle \int {\frac {dx}{\cos ^{n}cx}}={\frac {\sin cx}{c(n-1)cos^{n-1}cx}}+{\frac {n-2}{n-1}}\int {\frac {dx}{\cos ^{n-2}cx}}\qquad {\mbox{(}}n>1{\mbox{)}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2f94cbd2eafb3809e77a15be3725340ce84c39cc)
![{\displaystyle \int {\frac {dx}{1+\cos cx}}={\frac {1}{c}}\tan {\frac {cx}{2}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/478322b4056d8192a77bc75153738e2508453aa6)
![{\displaystyle \int {\frac {dx}{1-\cos cx}}=-{\frac {1}{c}}\cot {\frac {cx}{2}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/24e320bd9d4ec7e20248bbb72a2ab04ea060355c)
![{\displaystyle \int {\frac {x\;dx}{1+\cos cx}}={\frac {x}{c}}\tan {\frac {cx}{2}}+{\frac {2}{c^{2}}}\ln \left|\cos {\frac {cx}{2}}\right|}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d18ff5f4712370e7b333e04b0220acba13840b0)
![{\displaystyle \int {\frac {x\;dx}{1-\cos cx}}=-{\frac {x}{c}}\cot {\frac {cx}{2}}+{\frac {2}{c^{2}}}\ln \left|\sin {\frac {cx}{2}}\right|}](https://wikimedia.org/api/rest_v1/media/math/render/svg/62d94b8fcbba8f323b79bc40238f50ced144f145)
![{\displaystyle \int {\frac {\cos cx\;dx}{1+\cos cx}}=x-{\frac {1}{c}}\tan {\frac {cx}{2}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b785bd70c86d08bbb26514f8f2e5d5302886c140)
![{\displaystyle \int {\frac {\cos cx\;dx}{1-\cos cx}}=-x-{\frac {1}{c}}\cot {\frac {cx}{2}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c5924bce1ec5d6eae2f8ff87b166bea8199d3b46)
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cos
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មុំ
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cos
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ទ្រឹស្តីបទស៊ីនុស (ឬហៅថារូបមន្តស៊ីនុស) គឺជាកន្សោមនៃទ្រឹស្តីបទពីតាករ៖
![{\displaystyle c^{2}=a^{2}+b^{2}-2ab\cos C\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7c5f4795efade2b94b3e89df23c25488cd9ea6de)
ឬ៖
![{\displaystyle \cos C={\frac {a^{2}+b^{2}-c^{2}}{2ab}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4376c7f93bd1369f44b2e0566b8fc2fadb56b03e)
ដើម្បីស្រាយបញ្ជាក់ទ្រឹស្តីបទនេះគេចែកត្រីកោណជាពីរត្រីកោណកែង។ គេប្រើទ្រឹស្តីបទនេះដើម្បីកំណត់រកធាតុនៃត្រីកោណមួយខណៈដែលគេស្គាល់ប្រវែងជ្រុងពីរនិងមុំមួយនៃត្រីកោណ។