483 — 2484 — 2 и 4 .

483
Так как угол принадлежит 2 четверти, то его синус будет положительным
<img src="http://tex.z-dn.net/?f=%5Csin+%5Calpha+%3D+%5Csqrt%7B1-%5Ccos%5E2+%5Calpha+%7D+%3D+%5Csqrt%7B1-%28-+%5Cfrac%7B1%7D%7B3%7D%29%5E2%7D+%3D+%5Csqrt%7B+%5Cfrac%7B8%7D%7B9%7D%7D+%3D+%5Cfrac%7B2+%5Csqrt%7B2%7D+%7D%7B3%7D+» id=»TexFormula1″ onerror=»texError(this)» title=»sin alpha = sqrt{1-cos^2 alpha } = sqrt{1-(- frac{1}{3})^2} = sqrt{ frac{8}{9}} = frac{2 sqrt{2} }{3} » alt=»sin alpha = sqrt{1-cos^2 alpha } = sqrt{1-(- frac{1}{3})^2} = sqrt{ frac{8}{9}} = frac{2 sqrt{2} }{3} » align=»absmiddle» class=»latex-formula»>
<img src="http://tex.z-dn.net/?f=%5Ccos%28+%5Calpha+-+%5Cfrac%7B+%5Cpi+%7D%7B4%7D+%29%3D%5Ccos+%5Calpha+%5Ccos+%5Cfrac%7B+%5Cpi+%7D%7B4%7D%2B%5Csin+%5Calpha+%5Csin++%5Cfrac%7B+%5Cpi+%7D%7B4%7D%3D%0A-+%5Cfrac%7B1%7D%7B3%7D%5Ccdot+%5Cfrac%7B+%5Csqrt%7B2%7D+%7D%7B2%7D++%2B+%5Cfrac%7B2+%5Csqrt%7B2%7D+%7D%7B3%7D%5Ccdot+%5Cfrac%7B+%5Csqrt%7B2%7D+%7D%7B2%7D++%3D%0A%5C%5C%5C%0A%3D-++%5Cfrac%7B+%5Csqrt%7B2%7D+%7D%7B6%7D++%2B+%5Cfrac%7B4%7D%7B6%7D%3D+%5Cfrac%7B4-+%5Csqrt%7B2%7D+%7D%7B6%7D+» id=»TexFormula2″ onerror=»texError(this)» title=»cos( alpha — frac{ pi }{4} )=cos alpha cos frac{ pi }{4}+sin alpha sin  frac{ pi }{4}= - frac{1}{3}cdot frac{ sqrt{2} }{2}  + frac{2 sqrt{2} }{3}cdot frac{ sqrt{2} }{2}  = \ =-  frac{ sqrt{2} }{6}  + frac{4}{6}= frac{4- sqrt{2} }{6} » alt=»cos( alpha — frac{ pi }{4} )=cos alpha cos frac{ pi }{4}+sin alpha sin  frac{ pi }{4}= - frac{1}{3}cdot frac{ sqrt{2} }{2}  + frac{2 sqrt{2} }{3}cdot frac{ sqrt{2} }{2}  = \ =-  frac{ sqrt{2} }{6}  + frac{4}{6}= frac{4- sqrt{2} }{6} » align=»absmiddle» class=»latex-formula»>

484
<img src="http://tex.z-dn.net/?f=%5Ccos5+%5Cbeta+%5Ccos2+%5Cbeta+%2B%5Csin5+%5Cbeta+%5Csin2+%5Cbeta+%3D%5Ccos%285+%5Cbeta+-2+%5Cbeta+%29%3D%5Ccos3+%5Cbeta%0A%5C%5C%5C%0A%5Ccos%28+%5Cfrac%7B7+%5Cpi+%7D%7B5%7D%2B+%5Calpha++%29%5Ccos%28+%5Cfrac%7B2+%5Cpi+%7D%7B5%7D%2B+%5Calpha++%29%2B%5Csin%28+%5Cfrac%7B7+%5Cpi+%7D%7B5%7D%2B+%5Calpha++%29%5Csin%28+%5Cfrac%7B2+%5Cpi+%7D%7B5%7D%2B+%5Calpha++%29%3D%0A%5C%5C%5C%0A%3D%5Ccos%28+%5Cfrac%7B7+%5Cpi+%7D%7B5%7D%2B+%5Calpha++-+%5Cfrac%7B2+%5Cpi+%7D%7B5%7D-+%5Calpha++%29%3D%0A%5Ccos+%5Cpi+%3D-1» id=»TexFormula3″ onerror=»texError(this)» title=»cos5 beta cos2 beta +sin5 beta sin2 beta =cos(5 beta -2 beta )=cos3 beta \ cos( frac{7 pi }{5}+ alpha  )cos( frac{2 pi }{5}+ alpha  )+sin( frac{7 pi }{5}+ alpha  )sin( frac{2 pi }{5}+ alpha  )= \ =cos( frac{7 pi }{5}+ alpha  — frac{2 pi }{5}- alpha  )= cos pi =-1″ alt=»cos5 beta cos2 beta +sin5 beta sin2 beta =cos(5 beta -2 beta )=cos3 beta \ cos( frac{7 pi }{5}+ alpha  )cos( frac{2 pi }{5}+ alpha  )+sin( frac{7 pi }{5}+ alpha  )sin( frac{2 pi }{5}+ alpha  )= \ =cos( frac{7 pi }{5}+ alpha  — frac{2 pi }{5}- alpha  )= cos pi =-1″ align=»absmiddle» class=»latex-formula»>

Добавить комментарий

Ваш e-mail не будет опубликован. Обязательные поля помечены *

Adblock
detector