Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What does the cosine function measure?

1. opp/hyp

2. adj/hyp

3. hyp/adj

4. 1/tan(A)

The correct answer is: adj/hyp

The cosine function measures the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. This relationship is crucial in trigonometry, particularly in defining how angles relate to distances in various applications, including physics, engineering, and computer graphics. When considering a right triangle with an angle A, the side opposite to angle A is referred to as the opposite side, the side next to the angle A is the adjacent side, and the longest side of the triangle, which is opposite the right angle, is called the hypotenuse. The cosine of angle A is mathematically formalized as: \[ \cos(A) = \frac{\text{adjacent}}{\text{hypotenuse}} \] Understanding this definition is fundamental for solving problems involving right triangles and for applying the cosine function in various contexts, such as determining angle measures and distances in the coordinate plane. The other options, while they relate to trigonometric functions, represent different ratios or functions: - The ratio of opposite side to hypotenuse describes the sine function, not cosine. - The ratio hypotenuse to adjacent is not a standard trigonometric function. - The expression \(1/\tan(A)\) represents the cot