Question

Вычислите: tg(arcsin(-1/3)+пи/2)

Answer 1

Формулы:

$sinleft(arcsin xright)=x, -1leq xleq 1\cosleft(arcsin xright)=sqrt{1-x^2} , -1leq xleq 1$

$mathrm{tg}left(arcsinleft(-dfrac{1}{3}right)+dfrac{pi}{2}right)=-mathrm{ctg}left(arcsinleft(-dfrac{1}{3}right)right)=\=-dfrac{cosleft(arcsinleft(-frac{1}{3}right)right)}{sinleft(arcsinleft(-frac{1}{3}right)right)} =-dfrac{sqrt{1-left(-frac{1}{3}right)^2}}{-frac{1}{3}} =dfrac{sqrt{1-frac{1}{9}}}{frac{1}{3}}= dfrac{sqrt{frac{8}{9}}}{frac{1}{3}} =dfrac{sqrt{8}} {3}:dfrac{1}{3}=sqrt{8}$