# How do you find the other five trigonometric values given cos t = 5/13 and sin t > 0?

Jul 21, 2016

$\sec t = \frac{13}{5}$;$\sin t = \frac{12}{13}$;$\cos e c t = \frac{13}{12}$;$\tan t = \frac{5}{12}$$\cot t = \frac{12}{5}$

#### Explanation:

$\cos t = \frac{5}{13}$
$\sec t = \frac{1}{\cos} t = \frac{13}{5}$
$\sin t = \sqrt{1 - {\left(\frac{5}{13}\right)}^{2}}$
or
$\sin t = \sqrt{1 - \frac{25}{169}}$
or
$\sin t = \sqrt{\frac{169 - 25}{169}}$
or
$\sin t = \sqrt{\frac{144}{169}}$
or
$\sin t = \frac{12}{13}$
$\cos e c t = \frac{1}{\sin} t = \frac{13}{12}$
$\tan t = \sin \frac{t}{\cos} t = \frac{\frac{5}{13}}{\frac{12}{13}} = \frac{5}{12}$
$\cot t = \frac{1}{\tan} t = \frac{12}{5}$