Question 858255
Suppose sinθ = 1/4, and π/2 ≤ θ ≤ 2π. Find the exact value of cos θ. Explain steps please
Reference angle &#952; is in quadrant II in which cos<0
use x for  &#952;

{{{cos(x)=-sqrt(1-sin^2(x))=-sqrt(1-(1/4)^2)=-sqrt(1-(1/16))=-sqrt(15/16)=-sqrt(15)/4}}}
calculator check:
sin(x)=1/4
x&#8776;165.52&#730;
cos(x)=cos(165.52)&#8776;-0.9682…
exact value=-&#8730;15/4&#8776;-0.9682…