What is the value of cos 60°?

The value of cos 60° is indeed 0.5, and this can be understood through the properties of a right triangle and the unit circle. At 60 degrees, if you consider an equilateral triangle where each angle is 60 degrees, you can split this triangle in half, creating two 30-60-90 triangles. In such a triangle, the ratio of the lengths of the sides opposite the angles is well-established: the side opposite the 30-degree angle is half the length of the hypotenuse, while the side opposite the 60-degree angle is longer by a factor of √3.

When calculating cosine, which is the adjacent side over the hypotenuse in a right triangle, for the angle of 60 degrees, you observe that the adjacent side (the shorter side in this case) is half of the hypotenuse (where the hypotenuse is considered to be 1 for simplicity in the unit circle). Therefore, cos 60° = adjacent/hypotenuse = (1/2)/1 = 0.5.

This fundamental understanding of angles and triangle properties provides a solid foundation for trigonometric values, confirming that cos 60° equals 0.5.