# Given that t is in quadrant II and sin(t)=(7/25), how do you find the exact values of cos(t), tan(t), cot(t), sec(t), and csc(t)?

May 13, 2016

$\sin t = \frac{7}{25}$ --> ${\cos}^{2} t = 1 - {\sin}^{2} t = 1 - \frac{49}{625} = \frac{576}{25}$.
$\cos t = - \frac{24}{25}$ (cos t is negative because t is in Quadrant II).
$\tan t = \frac{\sin}{\cos} = \left(\frac{7}{25}\right) \left(- \frac{25}{24}\right) = - \frac{7}{24}$
$\cot t = \frac{1}{\tan} = - \frac{24}{7}$
$\sec t = \frac{1}{\cos} = - \frac{25}{24}$
$\csc t = \frac{1}{\sin} = \frac{25}{7}$