Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is cotangent in terms of sine and cosine?

1. tan(A)/sin(A)

2. 1/sin(A)

3. adj/opp

4. 1/tan(A)

The correct answer is: 1/tan(A)

Cotangent is defined in terms of sine and cosine as the ratio of the adjacent side to the opposite side in a right triangle, which can also be expressed mathematically using sine and cosine functions. The cotangent of an angle (denoted as cot(A)) is equal to the cosine of the angle divided by the sine of the angle. Thus, cot(A) can be written as: cot(A) = cos(A)/sin(A). Furthermore, since tangent (tan) is defined as sin(A)/cos(A), the cotangent can be rewritten using tangent as: cot(A) = 1/tan(A). This relationship highlights that the cotangent is the reciprocal of the tangent function, making option D a valid representation of cotangent in terms of tangent. This connection is crucial in trigonometry and is often used in various mathematical applications and identities. To provide additional context, the other options do not accurately represent cotangent. For instance, the expression involving the sine function does not capture the relationship correctly, and the option regarding adjacent and opposite sides lacks the appropriate mathematical formulation that includes sine and cosine. Understanding cotangent in this way is fundamental in trigonometric properties and identities.