To convert radians to degrees, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>180</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math> , since a full circle is <math><mstyle displaystyle="true"><mn>360</mn><mi>°</mi></mstyle></math> or <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> radians.

Simplify the numerator.

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.

Evaluate <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mn>5</mn><mo>)</mo></mrow></mstyle></math> to get <math><mstyle displaystyle="true"><mn>0.08748866</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0.08748866</mn></mstyle></math> to get <math><mstyle displaystyle="true"><mo>-</mo><mn>0.08748866</mn></mstyle></math> .

Evaluate <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mn>55</mn><mo>)</mo></mrow></mstyle></math> to get <math><mstyle displaystyle="true"><mn>1.42814800</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1.42814800</mn></mstyle></math> to get <math><mstyle displaystyle="true"><mo>-</mo><mn>1.42814800</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>1.42814800</mn></mstyle></math> from <math><mstyle displaystyle="true"><mo>-</mo><mn>0.08748866</mn></mstyle></math> to get <math><mstyle displaystyle="true"><mo>-</mo><mn>1.51563667</mn></mstyle></math> .

Simplify the denominator.

Remove parentheses.

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.

Evaluate <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mn>5</mn><mo>)</mo></mrow></mstyle></math> to get <math><mstyle displaystyle="true"><mn>0.08748866</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0.08748866</mn></mstyle></math> to get <math><mstyle displaystyle="true"><mo>-</mo><mn>0.08748866</mn></mstyle></math> .

Evaluate <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mn>55</mn><mo>)</mo></mrow></mstyle></math> to get <math><mstyle displaystyle="true"><mn>1.42814800</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>0.08748866</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1.42814800</mn></mstyle></math> to get <math><mstyle displaystyle="true"><mo>-</mo><mn>0.12494676</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>0.12494676</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> to get <math><mstyle displaystyle="true"><mn>0.87505323</mn></mstyle></math> .

Simplify the expression.

Divide <math><mstyle displaystyle="true"><mo>-</mo><mn>1.51563667</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0.87505323</mn></mstyle></math> to get <math><mstyle displaystyle="true"><mo>-</mo><mn>1.73205080</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1.73205080</mn></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><mn>180</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math> to get <math><mstyle displaystyle="true"><mo>-</mo><mn>1.73205080</mn><mfrac><mrow><mn>180</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mo>-</mo><mn>1.73205080</mn><mfrac><mrow><mn>180</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math> .

Write <math><mstyle displaystyle="true"><mo>-</mo><mn>1.73205080</mn></mstyle></math> as a fraction with denominator <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>1.73205080</mn></mrow><mrow><mn>1</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>180</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math> to get <math><mstyle displaystyle="true"><mfrac><mrow><mo>-</mo><mn>1.73205080</mn><mo>⋅</mo><mn>180</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1.73205080</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> to get <math><mstyle displaystyle="true"><mo>-</mo><mn>311.76914536</mn></mstyle></math> .

Move the negative in front of the fraction.

Factor <math><mstyle displaystyle="true"><mn>311.76914536</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>311.76914536</mn></mstyle></math> .

Multiply by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Separate fractions.

Replace <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> with an approximation.

Divide <math><mstyle displaystyle="true"><mn>311.76914536</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3.14159265</mn></mstyle></math> to get <math><mstyle displaystyle="true"><mn>99.23920117</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> to get <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>99.23920117</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> to get <math><mstyle displaystyle="true"><mn>99.23920117</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>99.23920117</mn></mstyle></math> to get <math><mstyle displaystyle="true"><mo>-</mo><mn>99.23920117</mn></mstyle></math> .

Convert to a decimal.

For angles smaller than <math><mstyle displaystyle="true"><mn>0</mn><mi>°</mi></mstyle></math> , add <math><mstyle displaystyle="true"><mn>360</mn><mi>°</mi></mstyle></math> to the angle until the angle is larger than <math><mstyle displaystyle="true"><mn>0</mn><mi>°</mi></mstyle></math> .

The angle is in the third quadrant.

Quadrant <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math>

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