The point $( 5,12 )$ is on the terminal side of an angle in standard position.Determine the exact value of $\sec \theta$ .
A) $\sec \theta = \frac { 5 } { 12 }$
B) $\sec \theta = \frac { 13 } { 5 }$
C) $\sec \theta = \frac { 12 } { 5 }$
D) $\sec \theta = - \frac { 5 } { 13 }$
E) $\sec \theta = - \frac { 5 } { 12 }$

Question

Quizplus · Accepted Answer

The secant of an angle $\theta$ in a right triangle is defined as the ratio of the hypotenuse to the adjacent side. Given the point $(5,12)$, we can form a right triangle with legs of lengths 5 (adjacent to $\theta$) and 12 (opposite to $\theta$), and a hypotenuse which can be found using the Pythagorean theorem: $\sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13$. Therefore, $\sec \theta = \frac{\text{hypotenuse}}{\text{adjacent}} = \frac{13}{5}$.

The Point (5,12)( 5,12 )(5,12) Is on the Terminal Side of an Angle in Standard

The Point $( 5,12 )$ Is on the Terminal Side of an Angle in Standard