Which of the following represents the cosine of 30°?

The cosine of 30° is accurately represented by the value √3/2. This value arises from fundamental properties of a 30-60-90 right triangle, which is a common reference in trigonometry.

In a 30-60-90 triangle, the sides are in a specific ratio: the side opposite the 30° angle is the shortest (1 unit), the side opposite the 60° angle is √3 units, and the hypotenuse is 2 units. Cosine is defined as the ratio of the length of the adjacent side to the hypotenuse. For the 30° angle, the side adjacent to this angle is the longer leg (√3) and the hypotenuse is 2.

Thus, applying the cosine definition:

cos(30°) = adjacent/hypotenuse = √3/2

This calculation confirms that the cosine of 30° equals √3/2, making this option the correct representation of the cosine of 30°.

The other values presented do not correspond to the cosine of 30°. For example, 0.5 represents cos(60°), 1 is the cosine of 0° (or angles like 360°), and