Предмет: Математика,
автор: Rojal
Помогите пожалуйста, срочно, уже 2 урок сижу!
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Ответы
Автор ответа:
0
1.
![sin( frac{x}{4}- frac{ pi }{6})= frac{1}{2}\
frac{x}{4}- frac{ pi }{6}=(-1)^karcsinfrac{1}{2}+ pi k, kin Z\
frac{x}{4}- frac{ pi }{6}=(-1)^kfrac{ pi }{6}+ pi k, kin Z\
frac{x}{4}=(-1)^kfrac{ pi }{6}+ frac{ pi }{6}+ pi k, kin Z\
x=(-1)^kfrac{ 2pi }{3}+ frac{2 pi }{3}+4 pi k, kin Z\](https://tex.z-dn.net/?f=sin%28+frac%7Bx%7D%7B4%7D-+frac%7B+pi+%7D%7B6%7D%29%3D+frac%7B1%7D%7B2%7D%5C%0Afrac%7Bx%7D%7B4%7D-+frac%7B+pi+%7D%7B6%7D%3D%28-1%29%5Ekarcsinfrac%7B1%7D%7B2%7D%2B+pi+k%2C+kin+Z%5C%0Afrac%7Bx%7D%7B4%7D-+frac%7B+pi+%7D%7B6%7D%3D%28-1%29%5Ekfrac%7B+pi+%7D%7B6%7D%2B+pi+k%2C+kin+Z%5C%0Afrac%7Bx%7D%7B4%7D%3D%28-1%29%5Ekfrac%7B+pi+%7D%7B6%7D%2B+frac%7B+pi+%7D%7B6%7D%2B+pi+k%2C+kin+Z%5C%0Ax%3D%28-1%29%5Ekfrac%7B+2pi+%7D%7B3%7D%2B+frac%7B2+pi+%7D%7B3%7D%2B4+pi+k%2C+kin+Z%5C "sin( frac{x}{4}- frac{ pi }{6})= frac{1}{2}\
frac{x}{4}- frac{ pi }{6}=(-1)^karcsinfrac{1}{2}+ pi k, kin Z\
frac{x}{4}- frac{ pi }{6}=(-1)^kfrac{ pi }{6}+ pi k, kin Z\
frac{x}{4}=(-1)^kfrac{ pi }{6}+ frac{ pi }{6}+ pi k, kin Z\
x=(-1)^kfrac{ 2pi }{3}+ frac{2 pi }{3}+4 pi k, kin Z\")
2.
![cos(4x+ frac{ pi }{4} )= frac{ sqrt{3} }{2} \
4x+ frac{ pi }{4}=pm arccosfrac{ sqrt{3} }{2}+2 pi k, kin Z\
4x+ frac{ pi }{4}=pm frac{ pi }{6} +2 pi k, kin Z\
4x=pm frac{ pi }{6} - frac{ pi }{4}+2 pi k, kin Z\
x=pm frac{ pi }{24} - frac{ pi }{16}+ frac{ pi k}{2} , kin Z\](https://tex.z-dn.net/?f=cos%284x%2B+frac%7B+pi+%7D%7B4%7D+%29%3D+frac%7B+sqrt%7B3%7D+%7D%7B2%7D+%5C%0A4x%2B+frac%7B+pi+%7D%7B4%7D%3Dpm+arccosfrac%7B+sqrt%7B3%7D+%7D%7B2%7D%2B2+pi+k%2C+kin+Z%5C%0A4x%2B+frac%7B+pi+%7D%7B4%7D%3Dpm++frac%7B+pi+%7D%7B6%7D+%2B2+pi+k%2C+kin+Z%5C%0A4x%3Dpm++frac%7B+pi+%7D%7B6%7D+-+frac%7B+pi+%7D%7B4%7D%2B2+pi+k%2C+kin+Z%5C%0Ax%3Dpm++frac%7B+pi+%7D%7B24%7D+-+frac%7B+pi+%7D%7B16%7D%2B+frac%7B+pi+k%7D%7B2%7D+%2C+kin+Z%5C "cos(4x+ frac{ pi }{4} )= frac{ sqrt{3} }{2} \
4x+ frac{ pi }{4}=pm arccosfrac{ sqrt{3} }{2}+2 pi k, kin Z\
4x+ frac{ pi }{4}=pm frac{ pi }{6} +2 pi k, kin Z\
4x=pm frac{ pi }{6} - frac{ pi }{4}+2 pi k, kin Z\
x=pm frac{ pi }{24} - frac{ pi }{16}+ frac{ pi k}{2} , kin Z\")
3.
![tg( frac{x}{8}- frac{ pi }{3} )= frac{ sqrt{3} }{3} \
frac{x}{8}- frac{ pi }{3}=arctgfrac{ sqrt{3} }{3}+ pi k, kin Z\
frac{x}{8}- frac{ pi }{3}= frac{ pi }{6} + pi k, kin Z\
frac{x}{8}= frac{ pi }{6}+frac{ pi }{3} + pi k, kin Z\
frac{x}{8}= frac{ pi }{2} + pi k, kin Z\
x=4 pi +8pi k, kin Z\](https://tex.z-dn.net/?f=tg%28+frac%7Bx%7D%7B8%7D-+frac%7B+pi+%7D%7B3%7D++%29%3D+frac%7B+sqrt%7B3%7D+%7D%7B3%7D+%5C%0Afrac%7Bx%7D%7B8%7D-+frac%7B+pi+%7D%7B3%7D%3Darctgfrac%7B+sqrt%7B3%7D+%7D%7B3%7D%2B+pi+k%2C+kin+Z%5C%0Afrac%7Bx%7D%7B8%7D-+frac%7B+pi+%7D%7B3%7D%3D+frac%7B+pi+%7D%7B6%7D+%2B+pi+k%2C+kin+Z%5C%0Afrac%7Bx%7D%7B8%7D%3D+frac%7B+pi+%7D%7B6%7D%2Bfrac%7B+pi+%7D%7B3%7D+%2B+pi+k%2C+kin+Z%5C%0Afrac%7Bx%7D%7B8%7D%3D+frac%7B+pi+%7D%7B2%7D+%2B+pi+k%2C+kin+Z%5C%0Ax%3D4+pi+%2B8pi+k%2C+kin+Z%5C "tg( frac{x}{8}- frac{ pi }{3} )= frac{ sqrt{3} }{3} \
frac{x}{8}- frac{ pi }{3}=arctgfrac{ sqrt{3} }{3}+ pi k, kin Z\
frac{x}{8}- frac{ pi }{3}= frac{ pi }{6} + pi k, kin Z\
frac{x}{8}= frac{ pi }{6}+frac{ pi }{3} + pi k, kin Z\
frac{x}{8}= frac{ pi }{2} + pi k, kin Z\
x=4 pi +8pi k, kin Z\")
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