Question

If O is an angle in standard position and its terminal side passes through the point(-12,-5), find the exact value of sec 0 in simplest radical form.

Answer 1

Ok, let's start by calculating the distance between the point and the origin, ok? Remember the origin is the point (0,0)

$d\text{ = }\sqrt[]{(-12-0)^2+(-5-0)^2}$

$\begin{gathered} d\text{ = }\sqrt[]{144\text{ + 25 }} \\ d=\text{ }\sqrt[]{169} \\ d\text{ = 13} \end{gathered}$

As the angle O is in standard position, adjacent leg = -12, opposite leg= -5 and hypotenuse = 13.

sec O = h/a

sec O= 13/-12

$\sec O=-1\frac{1}{12}$