Question

What is the frequency of the tangent function represented in the graph below?Graph1342

Answer 1

Answer: 4 (I got this right on the test)

Explanation:

The period of the graph is 2π – 7π/4 = π /4

The frequency for a tangent function is:

π/T (To find the frequency divide π by the period, T.)

π / π/4 = 4

Thus, the frequency for the tangent function above is 4

.

Answer 2

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:

`T=2\pi-(7\pi)/(4)=(8\pi-7\pi)/(4)=(\pi)/(4)`

The frequency f given the period T is :

`f=(1)/(T)`

Since T = π/4, it follows that:

`\begin{gathered} f=(1)/((\pi)/(4))=(4)/(\pi) \\ \text{ Therefore,} \\ f\approx1.2732\text{ Hz} \end{gathered}`

Therefore, the required frequency is approximately 1.2732 Hz