# If sin theta = -15/17 and theta is in the fourth quadrant, what is sec theta?

May 28, 2016

$\frac{17}{8}$
Use the trig identity: ${\cos}^{2} x = 1 - {\sin}^{2} x$
${\cos}^{2} t = 1 - {\sin}^{2} t = 1 - \frac{225}{278} = \frac{64}{278}$
$\cos t = \frac{8}{17}$ (in Quadrant 4, cos x is positive)
$\sec t = \frac{1}{\cos t} = \frac{17}{8}$