Find the Exact Value tan((21pi)/2+pi/2)

$\tan (\frac{21 π}{2} + \frac{π}{2})$

Combine the numerators over the common denominator.

$\tan (\frac{21 π + π}{2})$

Add $21 π$ and $π$ .

$\tan (\frac{22 π}{2})$

Cancel the common factor of $22$ and $2$ .

Factor $2$ out of $22 π$ .

$\tan (\frac{2 (11 π)}{2})$

Cancel the common factors.

Factor $2$ out of $2$ .

$\tan (\frac{2 (11 π)}{2 (1)})$

Cancel the common factor.

$\tan (\frac{2 (11 π)}{2 \cdot 1})$

Rewrite the expression.

$\tan (\frac{11 π}{1})$

Divide $11 π$ by $1$ .

$\tan (11 π)$

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\tan (π)$

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the second quadrant.

$- \tan (0)$

The exact value of $\tan (0)$ is $0$ .

$- 0$

Multiply $- 1$ by $0$ .

$0$

Find the Exact Value tan((21pi)/2+pi/2)

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