The exact value of cos 45 degrees is √2 / 2.
This value comes from the properties of a right triangle. In a 45-45-90 triangle, the legs are of equal length. Using the Pythagorean theorem, if we assume each leg has a length of 1, the hypotenuse will be √2. Therefore, the cosine of 45 degrees, which is the ratio of the length of the adjacent side to the hypotenuse, is:
cos(45°) = adjacent / hypotenuse = 1 / √2.
To express this in a more standard form, we can multiply the numerator and the denominator by √2, resulting in:
cos(45°) = (1 * √2) / (√2 * √2) = √2 / 2.
This value is crucial in trigonometry and is frequently used in various mathematical calculations.