QuestionFind the exact value of $\tan(11 \pi)$ without using a calculator.

Studdy Solution

STEP 1

Assumptions1. We are asked to find the exact value of $\tan (11 \pi)$ . . We know that the tangent function has a period of $\pi$ .

STEP 2

We use the periodicity of the tangent function to simplify the argument. Since the period of the tangent function is $\pi$ , we know that $\tan(x) = \tan(x + n\pi)$ , where $n$ is any integer.
$\tan (11 \pi) = \tan (11 \pi -11\pi)$

STEP 3

implify the expression within the tangent function.
$\tan (11 \pi -11\pi) = \tan (0)$

STEP 4

We know that the tangent of zero is zero.
$\tan (0) =0$ So, the exact value of $\tan (11 \pi)$ is0.

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