Trigonometric Ratio: Secant

Trigonometric Ratio: Secant

How to solve secant (trigonometric ratio) problems: definition, example, and its solution.

Definition

sec A = 1/cos A = (Hypotenuse) / (Adjacent side)

Secant is the reciprocal of cosine.

Cosine: CAH.
[cos A = (Adjacent side) / (Hypotenuse)]

So sec A = (Hypotenuse) / (Adjacent side).

Example

Find sec A. For a right triangle: Adjacent side: 1, Opposite side: 2

sec A = (hypotenuse) / (adjacent side)

In the given right triangle,
the hypotenuse is missing.

So find the hypotenuse
by using the Pythagorean theorem.

(hypotenuse) = √5

sec A = 1 / cos A

Cosine: CAH.
So cos A = 1/√5.

So, its reciprocal, secant is
sec A = √5/1.