Questions: The period of the tangent function is . (Type an exact answer, using π as needed.)

Transcript text: The period of the tangent function is $\square$ . (Type an exact answer, using $\pi$ as needed.)

Solution

Solution Steps

The period of the tangent function, $\tan(x)$, is the interval over which the function repeats itself. For the standard tangent function, this period is $\pi$.

Step 1: Identify the Function

The function in question is the tangent function, denoted as $ \tan(x) $.

Step 2: Determine the Period

The period of the tangent function is defined as the smallest positive value $ p $ such that: \[ \tan(x + p) = \tan(x) \] For the tangent function, this period is known to be $ \pi $.

Final Answer

The period of the tangent function is $ \boxed{\pi} $.

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