Math / Trigonometry

QuestionFill in the blank. The period of $y=\tan x$ is $\square$

Studdy Solution

STEP 1

1. The function $y = \tan x$ is a standard trigonometric function.
2. The period of a function is the smallest positive interval after which the function repeats its values.

STEP 2

1. Recall the definition of the period for trigonometric functions.
2. Identify the period of the tangent function.

STEP 3

Recall that the period of a trigonometric function is the smallest positive interval $P$ such that $f(x + P) = f(x)$ for all $x$ in the domain of $f$ .

STEP 4

The tangent function, $y = \tan x$ , has a period because it repeats its values at regular intervals. Specifically, the tangent function repeats every $\pi$ radians. Therefore, the period of $y = \tan x$ is $\pi$ .
The period of $y = \tan x$ is $\boxed{\pi}$ .

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