determine the period of the following graph. express your answer in simplest form.

Explanation:

Step1: Identify consecutive peaks

Observe the $x$-coordinates of two consecutive maximum points on the graph. $$x_{1} = 0, x_{2} = 2\pi$$

Step2: Calculate the horizontal distance

Subtract the first $x$-coordinate from the second to find the period. $$P = x_{2} - x_{1}$$

Step3: Compute the final value

Substitute the identified values into the subtraction formula. $$P = 2\pi - 0 = 2\pi$$

Answer:

2\pi