Question

stiind ca x∈(π,$\frac{3 pi}{2}$) si sinx=$\frac{-5}{13}$ sa se calculeze cos(2π-x)

Answer 1

x fiind in cadranul III, cosx<0, deci
$cosx=-\sqrt{1-sin^2x}=-\sqrt{1-\dfrac{25}{169}}=-\sqrt{\dfrac{144}{169}}=-\dfrac{12}{13}$

$cos(2\pi-x)=cosx =-\dfrac{12}{13}$