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

$$\frac{2\pi }{3}.$$