question determine the period of the following tangent graph. if necessary, write your answer as a fraction…

Explanation:

Step1: Recall tangent - function period formula

The period of the tangent function (y = A\tan(Bx - C)+D) is (T=\frac{\pi}{|B|}). For a tangent - graph, we can also find the period by looking at the horizontal distance between two consecutive vertical asymptotes.

Step2: Identify consecutive vertical asymptotes

From the graph, we can see that two consecutive vertical asymptotes are at (x =-\frac{\pi}{40}) and (x=\frac{\pi}{40}).

Step3: Calculate the period

The period (T) is the difference between the (x) - values of two consecutive vertical asymptotes. So (T=\frac{\pi}{40}-\left(-\frac{\pi}{40}\right)=\frac{\pi}{40}+\frac{\pi}{40}=\frac{\pi}{20}).

Answer:

(\frac{\pi}{20})