Secant: in a Right Triangle

How to find secant in a right triangle (trigonometry): formula, 1 example, and its solution.

Formula

Formula

Secant is the reciprocal of cosine.

So, to find secant (sec A),

first write 1/[cos A],

find cos A = (Adjacent side)/(Hypotenuse),

and write the reciprocal of cos A:
1 / [(Adjacent side)/(Hypotenuse)].

Example

Example

Solution

Secant is the reciprocal of cosine.

And cosine is CAH:
Cosine, Adjacent side, Hypotenuse.

But the hypotenuse is unknown.

So set the hypotenuse x
and find x first.

The given triangle is a right triangle.
So, by the Pythagorean theorem,
x2 = 12 + 22.

12 = 1

+22 = +4

1 + 4 = 5

x2 = 5

So x = √5.

Square Root

x is the hypotenuse.
So x is plus.
So you don't have to write ±.

Write √5
next to the hypotenuse.

sec A = 1/[cos A]

Find cos A.

Cosine is CAH:
Cosine,
Adjacent side (1),
Hypotenuse (√5).

So 1/[cos A] = 1/[1/√5].

1/[1/√5] = √5

The reciprocal of 1/√5 is
5/1 = √5.

So sec A = √5.