Trigonometry Examples

$\tan (\frac{- 14 π}{4})$

Step 1

Rewrite $\tan (\frac{- 14 π}{4})$ in terms of sines and cosines.

$\frac{\sin (\frac{- 14 π}{4})}{\cos (\frac{- 14 π}{4})}$

Step 2

Cancel the common factor of $- 14$ and $4$ .

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Step 2.1

Factor $2$ out of $- 14 π$ .

$\frac{\sin (\frac{- 14 π}{4})}{\cos (\frac{2 (- 7 π)}{4})}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $4$ .

$\frac{\sin (\frac{- 14 π}{4})}{\cos (\frac{2 (- 7 π)}{2 (2)})}$

Step 2.2.2

Cancel the common factor.

$\frac{\sin (\frac{- 14 π}{4})}{\cos (\frac{2 (- 7 π)}{2 \cdot 2})}$

Step 2.2.3

Rewrite the expression.

$\frac{\sin (\frac{- 14 π}{4})}{\cos (\frac{- 7 π}{2})}$

Step 3

Move the negative in front of the fraction.

$\frac{\sin (\frac{- 14 π}{4})}{\cos (- \frac{7 π}{2})}$

Step 4

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

$\frac{\sin (\frac{- 14 π}{4})}{\cos (\frac{π}{2})}$

Step 5

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

$\frac{\sin (\frac{- 14 π}{4})}{0}$

Step 6

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

Undefined