The exact value of cos 60 is 0.5.
To understand why, we can refer to the unit circle, where cosine values represent the x-coordinate of a point corresponding to a specific angle.
Cosine of 60 degrees can also be derived from the properties of an equilateral triangle. If you divide an equilateral triangle in half, you create a 30-60-90 triangle. In a 30-60-90 triangle, the side opposite the 60-degree angle is half the hypotenuse, which means:
– Hypotenuse = 1
– Side opposite 60° = √3/2
– Side opposite 30° = 1/2
The cosine of an angle is defined as the ratio of the length of the adjacent side to the hypotenuse. For cos 60 degrees:
cos(60°) = Adjacent / Hypotenuse = (1/2) / 1 = 0.5
This reveals that the exact value of cos 60 is indeed 0.5.