Question

Вычислить:
2) cos (a-П/4),если cos a=-1/3 П/2

Answer 1

$cosa=-frac{1}{3}\\frac{pi}{2} textless a textless pi quad to quad sina textgreater 0; ,; ; sina=+sqrt{1-cos^2a}\\sina=sqrt{1-frac{1}{9}}=frac{sqrt8}{3}=frac{2sqrt2}{3}\\cos(a-frac{pi}{4})=cosacdot cosfrac{pi}{4}+sinacdot sinfrac{pi}{4}=\\=-frac{1}{3}cdot frac{sqrt2}{2}+frac{2sqrt2}{3}cdot frac{sqrt2}{2}= frac{-sqrt2+4}{6} = frac{sqrt2cdot (2sqrt2-1)}{6} = frac{2sqrt2-1}{3sqrt2} approx 0,43$