# How do you express csc((10pi)/3) as a trig function of an angle in Quadrant I?

Mar 12, 2018

$- \csc \left(\frac{\pi}{3}\right)$

#### Explanation:

$\csc \left(\frac{10 \pi}{3}\right)$

$= - \sec \left(\frac{10 \pi}{3} - 2 \pi\right) = - \sec \left(\frac{4 \pi}{3}\right)$

$= - \sec \left(\frac{4 \pi}{3} - \pi\right)$

$= - \sec \left(\frac{\pi}{3}\right) \leftarrow \frac{\pi}{3} \text{ in first quadrant}$