Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What is the period of a sine graph?

The correct answer is: 2π

The period of a sine graph is 2π, which reflects the distance along the x-axis that it takes for the graph to complete one full cycle of its wave pattern. In the standard sine function, written as y = sin(x), the graph starts at the origin (0,0), rises to its maximum value of 1 at π/2, descends back to 0 at π, continues down to its minimum value of -1 at 3π/2, and returns to 0 at 2π. This entire sequence from 0 to 2π comprises one complete cycle of the sine function. Thus, every 2π radians, the sine function repeats its values, indicating that the wave pattern is periodic with a period of 2π. This fundamental property is essential for understanding the behavior of sine functions in trigonometry and is widely applicable in various fields including physics and engineering.