# How do you find the remaining trigonometric ratios if sec(theta) = -3.5 and pi/2< theta < pi?

$\sec x = \frac{1}{\cos} x = - 3.5 \to \cos x = \frac{1}{-} 3.5 = - 0.286$
${\sin}^{2} x = 1 - {\left(0.286\right)}^{2} = 0.92 \to \sin x = 0.96$
$\tan x = \frac{0.96}{-} 0.286 = - 3.36$
$\cot x = \frac{1}{-} 3.36 = 0.30$
$\csc x = \frac{1}{\sin x} = \frac{1}{0.96} = 1.04$