# If the point P on the unit circle that corresponds to a real number t is: [5/7, - 2sqrt(6)/7], how do you find csc(t)?

May 13, 2015

If $t$ correspond to the point $P \left(x , y\right)$ on the unit circle, then

$\csc t = \frac{1}{y}$

In this question, $y = \frac{2 \sqrt{6}}{7}$

So,
$\csc t = \frac{1}{\frac{2 \sqrt{6}}{7}}$

$= 1 \cdot \frac{7}{2 \sqrt{6}}$

$= \frac{7}{2 \sqrt{6}} \frac{\sqrt{6}}{\sqrt{6}}$

$= \frac{7 \sqrt{6}}{6}$