Question

What is the period of the function: f(x) = 2 sin (3x+pi/3) +5

Answer 1

To determine the period of the function \( f(x) = 2 \sin(3x + \frac{\pi}{3}) + 5 \), we focus on the sine function within the expression.

The general form of a sine function is \( \sin(kx) \), where \( k \) is a constant that affects the period of the function. The period \( P \) of the sine function is given by the formula:

\[
P = \frac{2\pi}{|k|}
\]

In our function, we have:

\[
f(x) = 2 \sin(3x + \frac{\pi}{3}) + 5
\]

Here, the term \( k \) corresponds to the coefficient of \( x \) in the argument of the sine function, which is \( 3 \).

Calculating the period:

\[
P = \frac{2\pi}{|3|} = \frac{2\pi}{3}
\]

Therefore, the period of the function \( f(x) \) is

\[
\frac{2\pi}{3}.
\]