# If cot theta=1.5 and theta is in quadrant 3, what is the value of sin theta?

May 24, 2016

-0.55

#### Explanation:

Use trig identity:
$1 + {\cot}^{2} t = \frac{1}{{\sin}^{2} t}$
$1 + 2.25 = \frac{1}{{\sin}^{2} t}$
${\sin}^{2} t = \frac{1}{3.25}$
$\sin t = \pm \frac{1}{1.80}$
Since t is in quadrant III, then sin t is negative -->
$\sin t = - \frac{1}{1.8} = - 0.55$