Question

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

Answer 1

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:

`\sec \theta=(c)/(b)`

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:

`\begin{gathered} H=\sqrt[]{5^2+12^2} \\ =\sqrt[]{25+144} \\ =\sqrt[]{169} \\ =13 \end{gathered}`

Therefore, the exact value of secθ is:

`(13)/(5)`