Subtract <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> from both sides of the equation.

Divide each term in <math><mstyle displaystyle="true"><mn>3</mn><mi>tan</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>=</mo><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>θ</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>θ</mi></mstyle></math> from inside the tangent.

Evaluate <math><mstyle displaystyle="true"><mi>arctan</mi><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</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>18.43494882</mn><mo>-</mo><mn>180</mn><mi>°</mi></mstyle></math> .

The resulting angle of <math><mstyle displaystyle="true"><mn>161.56505117</mn><mi>°</mi></mstyle></math> is positive and coterminal with <math><mstyle displaystyle="true"><mo>-</mo><mn>18.43494882</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>18.43494882</mn></mstyle></math> to find the positive angle.

Subtract <math><mstyle displaystyle="true"><mn>18.43494882</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>θ</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 the answers.

Do you know how to Solve for θ in Degrees 3tan(theta)+1=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.

Name | nine hundred seven million six hundred seven thousand one hundred seventy-six |
---|

- 907607176 has 32 divisors, whose sum is
**3500770752** - The reverse of 907607176 is
**671706709** - Previous prime number is
**7**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 43
- Digital Root 7

Name | one billion ninety-one million three hundred seventy-seven thousand seven hundred forty-five |
---|

- 1091377745 has 4 divisors, whose sum is
**1309653300** - The reverse of 1091377745 is
**5477731901** - Previous prime number is
**5**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 44
- Digital Root 8

Name | two billion seventy-six million two hundred thirty-eight thousand seven hundred ninety-seven |
---|

- 2076238797 has 8 divisors, whose sum is
**2770409856** - The reverse of 2076238797 is
**7978326702** - Previous prime number is
**1327**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 51
- Digital Root 6