Ohio Assessments for Educators (OAE) Mathematics Practice Exam

In terms of radians, what is the period of a tangent graph?

1. π

2. 2π

3. θ

4. 360

The correct answer is: π

The period of a tangent graph is π radians. The tangent function, defined as the ratio of the sine and cosine functions (tan(θ) = sin(θ)/cos(θ)), exhibits periodic behavior. Unlike sine or cosine functions that have a period of 2π radians, the tangent function completes one full cycle between -π/2 and π/2, repeating its pattern every π radians. This means that the values of tangent function return to their original value after π radians, confirming that this is the correct period for the tangent graph. For clarification on the context of the other potential answers, 2π is indeed the period for sine and cosine functions, but not for tangent. The choice of θ does not represent a defined period, and 360 degrees is a measure of angle rather than the period in radians, which is not relevant in this context since we are asked for the period specifically in radians.