Trigonometric Ratio: Cosine

Trigonometric Ratio: Cosine

How to solve cosine (trigonometric ratio) problems: definition, examples, and their solutions.

Definition

cos A = (Adjacent side) / (Hypotenuse). Remember: CAH (Cosine, Adjacent, and Hypotenuse).

Cosine is the ratio of a right triangle's
(Adjacent side) / (Hypotenuse).

CAH:
Cosine = (Adjacent) / (Hypotenuse)

Example 1

Find cos A. Hypotenuse: 5, The side opposite to angle A: 3, The side adjacent to angle A: 4.

Cosine: CAH.
So cos A = (Adjacent side, 4) / (Hypotenuse, 5).

Example 2

Find cos A. Hypotenuse: 13, The side opposite to angle A: 12, The side adjacent to angle A: 5.

Cosine: CAH.
So cos A = (Adjacent side, 5) / (Hypotenuse, 13).

Example 3

If cos A = 3/5, find the value of x. Hypotenuse: x, The side adjacent to angle A: 6.

Cosine: CAH.
So cos A = (Adjacent side, 6) / (Hypotenuse, x) = 3/5.