Question

what is the period of the function ( f(x) = -6 sin(3pi x + 4) - 2 )? give an exact value.
blank units

Explanation:

Step1: Recall the period formula for sine function

The general form of a sine function is \( f(x) = A\sin(Bx + C) + D \), and the period \( T \) of this function is given by the formula \( T=\frac{2\pi}{|B|} \).

Step2: Identify the value of \( B \) in the given function

In the function \( f(x)=- 6\sin(3\pi x + 4)-2 \), we can see that \( B = 3\pi \).

Step3: Calculate the period

Using the period formula \( T=\frac{2\pi}{|B|} \), substitute \( B = 3\pi \) into the formula. Since \( |3\pi|=3\pi \), we have \( T=\frac{2\pi}{3\pi} \). The \( \pi \) terms cancel out, and we get \( T = \frac{2}{3} \).

Answer:

\(\frac{2}{3}\)