# How do you find the values of the other trigonometric functions of theta from the information given tan theta = −3, and sin theta > 0?

May 6, 2015

Call tan x = t = -3, Use the trig identity: ${\cos}^{2} x = \frac{1}{1 + {t}^{2}}$
Since tan x = -3 is negative and sin x > 0, then x should be in quadrant II

${\cos}^{2} x = \frac{1}{1 + 9} = \frac{1}{10} = 0.10 \to \cos x = - 0.316$ (Quadrant II)

${\sin}^{2} x = 1 - {\cos}^{2} x = 1 - 0.10 = 0.90 \to \sin x = 0.95$ (Quadrant II)

cot x = - 1/3

$\sec = \frac{1}{\cos} x = \frac{1}{- 0.316} = - 3.16$

$\csc = \frac{1}{\sin} x = \frac{1}{0.95} = 1.05$