Trigonometry Examples

$\tan (\frac{21 π}{6})$

Step 1

Rewrite $\tan (\frac{21 π}{6})$ in terms of sines and cosines.

$\frac{\sin (\frac{21 π}{6})}{\cos (\frac{21 π}{6})}$

Step 2

Cancel the common factor of $21$ and $6$ .

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Step 2.1

Factor $3$ out of $21 π$ .

$\frac{\sin (\frac{21 π}{6})}{\cos (\frac{3 (7 π)}{6})}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $6$ .

$\frac{\sin (\frac{21 π}{6})}{\cos (\frac{3 (7 π)}{3 (2)})}$

Step 2.2.2

Cancel the common factor.

$\frac{\sin (\frac{21 π}{6})}{\cos (\frac{3 (7 π)}{3 \cdot 2})}$

Step 2.2.3

Rewrite the expression.

$\frac{\sin (\frac{21 π}{6})}{\cos (\frac{7 π}{2})}$

Step 3

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

$\frac{\sin (\frac{21 π}{6})}{\cos (\frac{3 π}{2})}$

Step 4

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\frac{\sin (\frac{21 π}{6})}{\cos (\frac{π}{2})}$

Step 5

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$\frac{\sin (\frac{21 π}{6})}{0}$

Step 6

The expression contains a division by $0$ . The expression is undefined.

Undefined