below is the graph of a trigonometric function. it intersects its mid - line at (4.7, - 3.8) and it has a…

below is the graph of a trigonometric function. it intersects its mid - line at (4.7, - 3.8) and it has a maximum point at (-4.7, 3.8). what is the period of the function? give an exact value.

below is the graph of a trigonometric function. it intersects its mid - line at (4.7, - 3.8) and it has a maximum point at (-4.7, 3.8). what is the period of the function? give an exact value.

Answer

Explanation:

Step1: Recall period - related property

The horizontal distance between a maximum point and the next - intersection with the mid - line is one - quarter of the period of a trigonometric function.

Step2: Calculate the horizontal distance

The x - coordinate of the maximum point is $x_1=-4.7$ and the x - coordinate of the mid - line intersection is $x_2 = 4.7$. The horizontal distance $d=\vert x_2 - x_1\vert=\vert4.7-(-4.7)\vert = 9.4$.

Step3: Find the period

Since $d=\frac{T}{4}$ (where $T$ is the period), then $T = 4d$. Substituting $d = 9.4$ into the formula, we get $T=4\times9.4 = 37.6$.

Answer:

$37.6$