Subtract <math><mstyle displaystyle="true"><msqrt><mn>13</mn></msqrt></mstyle></math> from both sides of the equation.

Divide each term in <math><mstyle displaystyle="true"><mn>5</mn><mi>tan</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow><mo>=</mo><mo>-</mo><msqrt><mn>13</mn></msqrt></mstyle></math> by <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Move the negative in front of the fraction.

Take the inverse tangent of both sides of the equation to extract <math><mstyle displaystyle="true"><mi>B</mi></mstyle></math> from inside the tangent.

Evaluate <math><mstyle displaystyle="true"><mi>arctan</mi><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><msqrt><mn>13</mn></msqrt></mrow><mrow><mn>5</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

The tangent function is negative in the second and fourth quadrants. To find the second solution, subtract the reference angle from <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> to find the solution in the third quadrant.

Add <math><mstyle displaystyle="true"><mn>360</mn><mi>°</mi></mstyle></math> to <math><mstyle displaystyle="true"><mo>-</mo><mn>35.79575991</mn><mo>-</mo><mn>180</mn><mi>°</mi></mstyle></math> .

The resulting angle of <math><mstyle displaystyle="true"><mn>144.20424008</mn><mi>°</mi></mstyle></math> is positive and coterminal with <math><mstyle displaystyle="true"><mo>-</mo><mn>35.79575991</mn><mo>-</mo><mn>180</mn></mstyle></math> .

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mn>180</mn></mrow><mrow><mrow><mo>|</mo><mi>b</mi><mo>|</mo></mrow></mrow></mfrac></mstyle></math> .

Replace <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> in the formula for period.

The absolute value is the distance between a number and zero. The distance between <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> to <math><mstyle displaystyle="true"><mo>-</mo><mn>35.79575991</mn></mstyle></math> to find the positive angle.

Subtract <math><mstyle displaystyle="true"><mn>35.79575991</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> .

List the new angles.

The period of the <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> degrees in both directions.

Consolidate <math><mstyle displaystyle="true"><mn>144.20424008</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>144.20424008</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> to <math><mstyle displaystyle="true"><mn>144.20424008</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> .

Do you know how to Solve for B in Degrees 5tan(B)+ square root of 13=0? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.