Rewrite <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mfrac><mrow><mo>-</mo><mn>14</mn><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> in terms of sines and cosines.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mn>14</mn><mi>π</mi></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Multiply <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> by <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Add full rotations of <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> until the angle is between <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

The expression contains a division by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> The expression is undefined.

Undefined

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