The period of the trigonometric function is 23/16 times the standard period, equivalent to 2π. The horizontal distance between consecutive midline intersections is 23/8π.
The period of a trigonometric function is the horizontal distance between two consecutive occurrences of a particular point in the graph, typically a peak, trough, or intercept. In this case, the function intersects its midline at (-7π, 2) and again at (-5/4π, 2). To find the period, we calculate the horizontal distance between these two points.
The difference between -7π and -5/4π is -7π - (-5/4π), which simplifies to -28/4π + 5/4π, resulting in -23/4π. Now, to find the period, we take the absolute value of this difference and divide by 2:
| -23/4π | / 2 = 23/8π.
Thus, the period of the function is 23/8π. However, it's important to note that the standard period for a trigonometric function is 2π. Therefore, to express the period in terms of the standard period, we can simplify the result:
(23/8π) / (2π) = 23/16.
So, the period of the function is 23/16 times the standard period, which is equivalent to 2π.