The period of a tangent function y = a tan(bx) is given by the distance between consecutive x-intercepts.
From the given graph, 2π and 7π/4 are consecutive x-intercepts.
Therefore, the period T of the function is given by:
[tex]T=2\pi-\frac{7\pi}{4}=\frac{8\pi-7\pi}{4}=\frac{\pi}{4}[/tex]
The frequency f given the period T is :
[tex]f=\frac{1}{T}[/tex]
Since T = π/4, it follows that:
[tex]\begin{gathered} f=\frac{1}{\frac{\pi}{4}}=\frac{4}{\pi} \\ \text{ Therefore,} \\ f\approx1.2732\text{ Hz} \end{gathered}[/tex]
Therefore, the required frequency is approximately 1.2732 Hz
