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Ответ дал:
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тригонометрические функции периодчны, у них период 2пи, поэтому достаточно забрать все целые периоды, и тогда будет ясно что за угол
![frac{27pi}{4}= frac{24pi+3pi}{4}=6pi+ frac{3pi}{4}:\
sin(frac{27pi}{4})=sin(frac{3pi}{4})= frac{ sqrt{2} }{2};\
cos(frac{27pi}{4})=cos(frac{3pi}{4})= frac{ sqrt{2} }{2};\
\
frac{35pi}{3}= frac{36pi-pi}{3}=12pi- frac{pi}{3}:\
sin(frac{35pi}{3})=sin(-frac{pi}{3})= -frac{ sqrt{3} }{2};\
cos(frac{35pi}{3})=cos(frac{pi}{3})= frac{ 1 }{2};\](https://tex.z-dn.net/?f=+frac%7B27pi%7D%7B4%7D%3D+frac%7B24pi%2B3pi%7D%7B4%7D%3D6pi%2B+frac%7B3pi%7D%7B4%7D%3A%5C%0A+++sin%28frac%7B27pi%7D%7B4%7D%29%3Dsin%28frac%7B3pi%7D%7B4%7D%29%3D+frac%7B+sqrt%7B2%7D+%7D%7B2%7D%3B%5C%0A++cos%28frac%7B27pi%7D%7B4%7D%29%3Dcos%28frac%7B3pi%7D%7B4%7D%29%3D+frac%7B+sqrt%7B2%7D+%7D%7B2%7D%3B%5C%0A%5C%0A+frac%7B35pi%7D%7B3%7D%3D+frac%7B36pi-pi%7D%7B3%7D%3D12pi-+frac%7Bpi%7D%7B3%7D%3A%5C%0A+++sin%28frac%7B35pi%7D%7B3%7D%29%3Dsin%28-frac%7Bpi%7D%7B3%7D%29%3D+-frac%7B+sqrt%7B3%7D+%7D%7B2%7D%3B%5C%0A++cos%28frac%7B35pi%7D%7B3%7D%29%3Dcos%28frac%7Bpi%7D%7B3%7D%29%3D+frac%7B+1+%7D%7B2%7D%3B%5C%0A "frac{27pi}{4}= frac{24pi+3pi}{4}=6pi+ frac{3pi}{4}:\
sin(frac{27pi}{4})=sin(frac{3pi}{4})= frac{ sqrt{2} }{2};\
cos(frac{27pi}{4})=cos(frac{3pi}{4})= frac{ sqrt{2} }{2};\
\
frac{35pi}{3}= frac{36pi-pi}{3}=12pi- frac{pi}{3}:\
sin(frac{35pi}{3})=sin(-frac{pi}{3})= -frac{ sqrt{3} }{2};\
cos(frac{35pi}{3})=cos(frac{pi}{3})= frac{ 1 }{2};\")
![frac{17pi}{3}= frac{12pi+5pi}{3}=4pi+ frac{5pi}{3}:\
sin(frac{17pi}{3})=sin(frac{5pi}{3})= -frac{ sqrt{3} }{2};\
cos(frac{17pi}{3})=cos(frac{5pi}{3})= frac{1 }{2};\
\
frac{23pi}{6}= frac{24pi-pi}{6}=4pi-frac{pi}{6}:\
sin(frac{23pi}{6})=sin(-frac{pi}{6})= -frac{1 }{2};\
cos(frac{23pi}{6})=cos(-frac{pi}{6})= frac{ sqrt{3} }{2};\](https://tex.z-dn.net/?f=+frac%7B17pi%7D%7B3%7D%3D+frac%7B12pi%2B5pi%7D%7B3%7D%3D4pi%2B+frac%7B5pi%7D%7B3%7D%3A%5C%0A+++sin%28frac%7B17pi%7D%7B3%7D%29%3Dsin%28frac%7B5pi%7D%7B3%7D%29%3D+-frac%7B+sqrt%7B3%7D+%7D%7B2%7D%3B%5C%0A++cos%28frac%7B17pi%7D%7B3%7D%29%3Dcos%28frac%7B5pi%7D%7B3%7D%29%3D+frac%7B1+%7D%7B2%7D%3B%5C%0A%5C%0A+frac%7B23pi%7D%7B6%7D%3D+frac%7B24pi-pi%7D%7B6%7D%3D4pi-frac%7Bpi%7D%7B6%7D%3A%5C%0A+++sin%28frac%7B23pi%7D%7B6%7D%29%3Dsin%28-frac%7Bpi%7D%7B6%7D%29%3D+-frac%7B1+%7D%7B2%7D%3B%5C%0A++cos%28frac%7B23pi%7D%7B6%7D%29%3Dcos%28-frac%7Bpi%7D%7B6%7D%29%3D+frac%7B+sqrt%7B3%7D+%7D%7B2%7D%3B%5C "frac{17pi}{3}= frac{12pi+5pi}{3}=4pi+ frac{5pi}{3}:\
sin(frac{17pi}{3})=sin(frac{5pi}{3})= -frac{ sqrt{3} }{2};\
cos(frac{17pi}{3})=cos(frac{5pi}{3})= frac{1 }{2};\
\
frac{23pi}{6}= frac{24pi-pi}{6}=4pi-frac{pi}{6}:\
sin(frac{23pi}{6})=sin(-frac{pi}{6})= -frac{1 }{2};\
cos(frac{23pi}{6})=cos(-frac{pi}{6})= frac{ sqrt{3} }{2};\")
Ответ дал:
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в косинусе 27пи/4 . пересчитайте пожалуйста . у меня получилось с противоположным знаком.
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