What is the exact value of sec -330?

May 6, 2018

$\sec \left(- 330\right) = \frac{2 \sqrt{3}}{3}$

Explanation:

$\sec \left(- 330\right)$

$- 330 \text{ }$will be in the first quadrant

$- 330 = + 30$

$\therefore \sec \left(- 330\right) = \sec 30$

$\sec 30 = \frac{1}{\cos} 30$

$\because \cos 30 = \frac{\sqrt{3}}{2}$

$\sec 30 = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}}$

rationalising

$\sec 30 = \frac{2 \sqrt{3}}{3}$