determine the period of the following tangent graph. if necessary, write your answer as a fraction in…
determine the period of the following tangent graph. if necessary, write your answer as a fraction in simplified form.
Answer
Explanation:
Step1: Identify period - definition
The period of a tangent function is the horizontal distance between two consecutive vertical asymptotes.
Step2: Locate consecutive asymptotes
From the graph, two consecutive vertical asymptotes are at $x =-\frac{\pi}{80}$ and $x=\frac{7\pi}{80}$.
Step3: Calculate the period
The period $P$ is given by $P=\frac{7\pi}{80}-\left(-\frac{\pi}{80}\right)=\frac{7\pi + \pi}{80}=\frac{8\pi}{80}=\frac{\pi}{10}$.
Answer:
$\frac{\pi}{10}$