Bestimmung von Tief- und Wendepunkten einer trigonometrischen Funktion

In this problem, we are given a trigonometric function with adjacent high points, H one and H two, and an amplitude of two. We need to find the coordinates of the low point and a point of inflection located between these two peaks.

Let's start by finding the low point. For a periodic trigonometric function, the low point, or minimum, lies exactly halfway between two adjacent high points horizontally.

We calculate the x-coordinate of the low point by taking the average of the x-coordinates of the two peaks.

The numerator sums to four pi over two, which is two pi. Dividing by two gives us pi.

Now for the vertical position. If the high point is at three and the amplitude is two, the vertical shift of the function's center line must be one. Subtracting another amplitude takes us to the low point.

Since the peaks are at y equals three and the distance from peak to trough is twice the amplitude, we subtract four from three.

Combining these, the low point T is located at pi and negative one.