Find the exact value of cos(45°).

The angle 45° appears in a 45°-45°-90° triangle.

The side lengths of a 45°-45°-90° triangle follow the ratio:
1 : 1 : √2

For either 45° angle, the adjacent leg has length 1 and the hypotenuse has length √2.

Using the cosine ratio:
cos(45°) = adjacent / hypotenuse

cos(45°) = 1 / √2

Rationalize the denominator by multiplying by √2/√2:
cos(45°) = √2 / 2

Therefore, the exact value of cos(45°) is √2/2.