The secant of an angle in a right triangle is given by the quotient of the length of the hypotenuse to the length of the side adjacent to it:
[tex]\sec \theta=\frac{c}{b}[/tex]
On the coordinate plane, the point (5,12) detmines a right triangle with sides 5 and 12:
Use the Pythagorean Theorem to find the length of the hypotenuse:
[tex]\begin{gathered} H=\sqrt[]{5^2+12^2} \\ =\sqrt[]{25+144} \\ =\sqrt[]{169} \\ =13 \end{gathered}[/tex]
Therefore, the exact value of secθ is:
[tex]\frac{13}{5}[/tex]
