Find the period of the function f(x)=|sin x|

The function \( f(x) = |\sin x| \) is derived from the sine function, which has a specific periodic behavior. To determine the period of \( f(x) \), we need to analyze how the absolute value affects the sine wave.

Understanding the Sine Function

The sine function, \( \sin x \), has a period of \( 2\pi \). This means it repeats its values every \( 2\pi \) units along the x-axis.

Effect of Absolute Value

When we take the absolute value of \( \sin x \), the negative parts of the sine wave are reflected above the x-axis. This transformation does not change the overall periodicity but alters the appearance of the graph.

Determining the New Period

Since \( |\sin x| \) is non-negative, it effectively repeats every \( \pi \) units instead of \( 2\pi \). This is because the function goes through one complete cycle of positive and negative values in the interval \( [0, \pi] \) and then mirrors that cycle in \( [\pi, 2\pi] \).

Final Result

Thus, the period of the function \( f(x) = |\sin x| \) is:

• Period: \( \pi \)