Ohio Assessments for Educators (OAE) Mathematics Practice Exam

The cosine of 30 degrees is indeed √3/2, which can be understood by utilizing the properties of a 30-60-90 triangle. In such a triangle, the ratios of the lengths of the sides are well-defined: the side opposite the 30-degree angle is half of the hypotenuse, and the side opposite the 60-degree angle is √3/2 times the hypotenuse.

To visualize this, if we consider a 30-60-90 triangle where the hypotenuse is of length 2, the side opposite the 30-degree angle would be 1 (half of the hypotenuse), and the side opposite the 60-degree angle would be √3. The cosine function, which is defined as the ratio of the length of the adjacent side to the hypotenuse, can thus be calculated as follows:

Cosine of 30 degrees = (length of adjacent side) / (length of hypotenuse) = (√3) / (2).

This shows that the value of cosine at 30 degrees aligns with the ratio we determined. Therefore, understanding the properties of special triangles aids in accurately determining trigonometric values like cosine.