Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What is the sine of angle x expressed as in terms of tangent?

sin(x) = cos(x) / tan(x)
tan(x) = sin(x) / cos(x)
sin(x) = tan(x) / cos(x)
tan(x) = cos(x) / sin(x)

The correct answer is: tan(x) = sin(x) / cos(x)

The relationship between sine and tangent can be derived from the definitions of these trigonometric functions. The tangent of an angle is defined as the ratio of the sine of that angle to the cosine of that angle. Therefore, if we express this mathematically, we have: tan(x) = sin(x) / cos(x). This equation indicates that the sine of angle x can be expressed in terms of tangent and cosine. To isolate sine, we can manipulate this equation: sin(x) = tan(x) * cos(x). This emphasizes the connection between sine and tangent, recognizing that tangent combines both sine and cosine. Understanding this fundamental relationship is essential, as it allows us to transition between different trigonometric functions depending on the given conditions of a problem. The other options do not provide the correct relationships or would imply incorrect identities among sine, cosine, and tangent.