# How do you use special angles to find the ratios of sec 180 degrees?

Nov 12, 2015

$\sec \left({180}^{\circ}\right) = - 1$

#### Explanation:

${180}^{\circ}$ has a reference angle of ${0}^{\circ}$ and falls along the negative X-axis.

$\textcolor{w h i t e}{\text{XXX}}$the $\text{hypotenuse}$ is always positive.
$\textcolor{w h i t e}{\text{XXX}}$the $\text{adjacent}$ is the X-axis value and along the negative X-axis it is negative.
For an angle of ${0}^{\circ}$ the lengths of the $\text{hypotenuse}$ and $\text{adjacent}$ sides are equal.
Therefore $\sec \left({180}^{\circ}\right) = - \sec \left({0}^{\circ}\right) = - 1$