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 | one billion eight hundred fifty-seven million seven hundred thirty thousand six hundred thirty-six |
---|

- 1857730636 has 16 divisors, whose sum is
**4180635000** - The reverse of 1857730636 is
**6360377581** - Previous prime number is
**6091**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 46
- Digital Root 1

Name | eight hundred thirty-seven million five hundred thirteen thousand four hundred seventy-two |
---|

- 837513472 has 512 divisors, whose sum is
**21464560818** - The reverse of 837513472 is
**274315738** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 40
- Digital Root 4

Name | one hundred one million ninety-two thousand four hundred sixteen |
---|

- 101092416 has 512 divisors, whose sum is
**1541187648** - The reverse of 101092416 is
**614290101** - Previous prime number is
**311**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 24
- Digital Root 6