What is the cosine of 60 degrees?

The cosine of 60 degrees is 0.5, which can be understood through both its geometric and trigonometric properties.

In the unit circle, the angle of 60 degrees corresponds to the point at coordinates (1/2, √3/2). The cosine of an angle is defined as the x-coordinate of the point on the unit circle that corresponds to that angle. Thus, for 60 degrees, the x-coordinate is 1/2, which is equivalent to 0.5.

Furthermore, from the perspective of a 30-60-90 right triangle, we can derive this value. In such a triangle, the ratios of the lengths of the sides are well-known: the side opposite the 30-degree angle is half the length of the hypotenuse, whereas the side opposite the 60-degree angle is √3/2 times the hypotenuse. As a result, when we look for the cosine of the 60-degree angle (which is the adjacent side over the hypotenuse), it yields 1/2.

Understanding these relationships shows why the cosine of 60 degrees is indeed 0.5, confirming that it is the correct answer.