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.

The exact value of <math><mstyle displaystyle="true"><mi>arctan</mi><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>3</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mo>-</mo><mn>30</mn></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>30</mn><mo>-</mo><mn>180</mn><mi>°</mi></mstyle></math> .

The resulting angle of <math><mstyle displaystyle="true"><mn>150</mn><mi>°</mi></mstyle></math> is positive and coterminal with <math><mstyle displaystyle="true"><mo>-</mo><mn>30</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>30</mn></mstyle></math> to find the positive angle.

Subtract <math><mstyle displaystyle="true"><mn>30</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 tan(theta)=(- square root of 3)/3? 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 | two billion one hundred thirty-four million five hundred sixty-nine thousand eight hundred eighty-two |
---|

- 2134569882 has 32 divisors, whose sum is
**4419334080** - The reverse of 2134569882 is
**2889654312** - Previous prime number is
**1931**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 48
- Digital Root 3

Name | one hundred fifty-eight million one hundred sixty-one thousand one hundred six |
---|

- 158161106 has 8 divisors, whose sum is
**237295344** - The reverse of 158161106 is
**601161851** - Previous prime number is
**9931**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 29
- Digital Root 2

Name | one billion three hundred ninety-three million ten thousand six hundred ninety-six |
---|

- 1393010696 has 64 divisors, whose sum is
**4787552952** - The reverse of 1393010696 is
**6960103931** - Previous prime number is
**193**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 38
- Digital Root 2