Given secθ=6/5 and tanθ<0, how do you find the values of the other five trigonometric functions?

Nov 2, 2015

Find 6 trig function values, knowing sec $x = \frac{6}{5}$ and tan x < 0.

Explanation:

$\sec x = \frac{6}{5}$--> $\cos x = \frac{5}{6}$ --> arc $x = \pm {33}^{\circ} 56.$
Since tan x < 0, then $x = - {33}^{\circ} 56.$
sin (- 33.56) = - 0.55
$\tan \left(- 33.56\right) = - \frac{0.55}{0.83} = - 0.66$
$\cot \left(- 33.56\right) = \frac{1}{\tan} = - 1.51$
$\sec \left(- 33.56\right) = \frac{6}{5}$
$\csc \left(- 33.56\right) = \frac{1}{\sin} = \frac{1}{-} 0.55 = - 1.82$