Questions: Use the unit circle to find the value of tan π and even or odd trigonometric functions to find the value of tan (−π). Select the correct choice below and fill in any answer boxes within your choice. A. tan π=0 (Type an exact answer, using radicals as needed. Simplify your answer. Rationalize the denominator.) B. The expression is undefined. Select the correct choice below and fill in any answer boxes within your choice. A. tan(−π)= (Type an exact answer, using radicals as needed. Simplify your answer. Rationalize the denominator.) B. The expression is undefined.

Use the unit circle to find the value of tan π and even or odd trigonometric functions to find the value of tan (−π). Select the correct choice below and fill in any answer boxes within your choice. A. tan π=0 (Type an exact answer, using radicals as needed. Simplify your answer. Rationalize the denominator.) B. The expression is undefined. Select the correct choice below and fill in any answer boxes within your choice. A. tan(−π)= (Type an exact answer, using radicals as needed. Simplify your answer. Rationalize the denominator.) B. The expression is undefined.
Transcript text: Use the unit circle to find the value of $\tan \pi$ and even or odd trigonometric functions to find the value of $\tan (-\pi)$. Select the correct choice below and fill in any answer boxes within your choice. A. $\boldsymbol{\operatorname { t a n }} \pi=0$ (Type an exact answer, using radicals as needed. Simplify your answer. Rationalize the denominator.) B. The expression is undefined. Select the correct choice below and fill in any answer boxes within your choice. A. $\boldsymbol{\operatorname { t a n }}(-\pi)=$ $\square$ (Type an exact answer, using radicals as needed. Simplify your answer. Rationalize the denominator.) B. The expression is undefined.
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Solution

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Solution Steps

Step 1: Find the coordinates corresponding to the angle

The angle $x$ is $\pi$ radians. On the unit circle, the coordinates corresponding to $\pi$ are $(-1,0)$.

Step 2: Calculate tan(x)

The tangent of an angle is defined as the ratio of the y-coordinate to the x-coordinate. Thus, $\tan(\pi) = \frac{0}{-1} = 0$.

Step 3: Calculate tan(-x)

Since tangent is an odd function, $\tan(-x) = -\tan(x)$. Therefore, $\tan(-\pi) = -\tan(\pi) = -0 = 0$.

Final Answer

$\tan(x) = 0$

$\tan(-x) = 0$

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