# How do you find the remaining trigonometric functions of theta given sintheta=-20/29 and theta terminates in QIII?

${\cos}^{2} t = 1 - {\sin}^{2} t = 1 - \frac{400}{841} = \frac{441}{841}$
$\cos t = \pm \frac{21}{29}$
$\cos t = - \frac{21}{19}$
$\tan t = \frac{\sin}{\cos} = \left(- \frac{20}{29}\right) \left(- \frac{29}{21}\right) = \frac{20}{21}$
$\cot t = \frac{1}{\tan} = \frac{21}{20}$
$\sec t = \frac{1}{\cos} = - \frac{19}{21}$
$\csc t = \frac{1}{\sin} = - \frac{29}{20}$