Question

Se sen h= 1/4 , com π/2 < h < π , concluímos que sec h vale *

a- (4√15)/15
b- √15/4
c- (15√15)/4
d- (4√15)/15
e- √15/4

Answer 1

Resposta:

$sen(x)=\frac{1}{4}$

$\frac{\pi }{2} <x<\pi$

$sec(x)=\frac{1}{cos(x)}$

Como, $\frac{\pi }{2} <x<\pi$ então:

$cos(x)<0$

$cos^2(x)=1-sen^2(x)$ $<=>$

$<=>cos^2(x)=1-(\frac{1}{4} )^2<=>$

$<=>cos^2(x)=1-\frac{1}{16} <=>$

$<=>cos^2(x)=\frac{15}{16} <=>$

$<=>cos(x)=+-\sqrt{\frac{15}{16} } =-\frac{\sqrt{15} }{4}$

$sec(x)=\frac{1}{-\frac{\sqrt{15} }{4} } =-\frac{4}{\sqrt{15} } =-\frac{4\sqrt{15} }{15}$