# How do you find the exact value of sec120?

##### 1 Answer
Mar 8, 2017

$\sec {120}^{\circ} = - 2$

#### Explanation:

Using the $\textcolor{b l u e}{\text{trigonometric identity}}$

color(red)(bar(ul(|color(white)(2/2)color(black)(sectheta=1/costheta;costheta≠0)color(white)(2/2)|)))

$\Rightarrow \sec {120}^{\circ} = \frac{1}{\cos} {120}^{\circ}$

$\text{now } \cos {120}^{\circ} = - \cos {60}^{\circ} = - \frac{1}{2}$

$\Rightarrow \sec {120}^{\circ} = \frac{1}{- \frac{1}{2}} = - 2$