# If sinA = -2/5 and tan θ > 0, then what are the five other trigonometric ratios?

Apr 12, 2016

$\cos A = - \frac{\sqrt{21}}{5}$

#### Explanation:

$\sin A = - \frac{2}{5}$. Find cos A by the identity:
${\cos}^{2} A = 1 - {\sin}^{2} A$
${\cos}^{2} A = 1 - \frac{4}{25} = \frac{21}{25}$ ---> $\cos A = \pm \frac{\sqrt{21}}{5}$
Since tan A > 0, then $\cos A = - \frac{\sqrt{21}}{5}$
$\tan A = \frac{\sin A}{\cos A} = \left(\frac{2}{5}\right) \left(\frac{5}{\sqrt{21}}\right) = \frac{2}{\sqrt{21}}$
The other trig ratios are:
$\cot A = \frac{\sqrt{21}}{2}$
$\sec A = \frac{1}{\cos} A = - \frac{5}{\sqrt{21}}$
$\csc A = \frac{1}{\sin} A = - \frac{5}{2}$