Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What is the period of a cosine graph?

The correct answer is: 2π

The period of a cosine graph refers to the length of one complete cycle of the cosine function on the x-axis. For the standard cosine function, written as $ y = \cos(x) $, one complete cycle occurs as the input $ x $ moves from 0 to $ 2\pi $ radians. During this interval, the graph starts at its maximum value (1), decreases to zero, reaches its minimum value (-1), returns to zero, and then returns to the maximum value. Thus, the length of this interval – from 0 to $ 2\pi $ – represents the period of the function. Therefore, the value that represents the period of a cosine graph is $ 2\pi $. This periodic nature means that the cosine graph will repeat its values every $ 2\pi $ radians along the x-axis. In contrast, choices such as $ \pi $ represent only half a cycle, making them insufficient to describe the full behavior of the cosine function. The letter $ \theta $ does not quantify any length or cycle but is typically used as a variable in trigonometric contexts. Lastly, 360 degrees, while representing a full cycle in degrees, does not