# If tanx= -2/9 and sinx>0 what are the remaining trigonometric functions?

May 6, 2018

As below.

#### Explanation:

$\text{Given : } \tan x = - \frac{2}{9}$

$\tan \theta = \text{(Opp. side) / (Adj. side)} = - \frac{2}{9}$

$\text{tan is negative in II & IV Quadrants}$

$\text{Hypotenuse } = \sqrt{{2}^{2} + {9}^{2}} = 9.22$

color(red)(" Case 1 : "

Values of other trigonometric functions when tan x in II Quadrant :

$\cot x = - \frac{9}{2}$

$\sin x = \frac{2}{9.22} , \csc x = \frac{1}{\sin} x = 4.61$

$\cos x = - \frac{9}{9.22} , \sec x = - \frac{9.22}{9}$

color(blue)(" Case 2 : "

Values of other trigonometric functions when tan x in IV Quadrant :

$\cot x = - \frac{9}{2}$

$\sin x = - \frac{2}{9.22} , \csc x = \frac{1}{\sin} x = - 4.61$

$\cos x = \frac{9}{9.22} , \sec x = \frac{9.22}{9}$