Question

determine whether the given function is periodic. if so, find its fundamental period p
7 + sin 10x
find the functions fundamental period. select the correct answer below and, if necessary, fill in the answer box to complete your choice
a. the fundamental period p is
(type an exact answer, using π as needed.)
b. the function is not periodic.

Explanation:

Step1: Recall the period formula for sine function

The general form of a sine function is \(y = A\sin(Bx - C)+D\), and its period \(T=\frac{2\pi}{|B|}\). For the function \(y = 7+\sin(10x)\), here \(B = 10\).

Step2: Calculate the period

Using the formula \(T=\frac{2\pi}{|B|}\), substitute \(B = 10\) into it. We get \(T=\frac{2\pi}{10}=\frac{\pi}{5}\).

Answer:

A. The fundamental period \(P\) is \(\frac{\pi}{5}\)