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

The exact value of <math><mstyle displaystyle="true"><mi>arccsc</mi><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><mn>2</mn><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>60</mn></mstyle></math> .

The cosecant function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> , to find a reference angle. Next, add this reference angle to <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> to find the solution in the third quadrant.

Subtract <math><mstyle displaystyle="true"><mn>360</mn><mi>°</mi></mstyle></math> from <math><mstyle displaystyle="true"><mn>360</mn><mo>+</mo><mn>60</mn><mo>+</mo><mn>180</mn><mi>°</mi></mstyle></math> .

The resulting angle of <math><mstyle displaystyle="true"><mn>240</mn><mi>°</mi></mstyle></math> is positive, less than <math><mstyle displaystyle="true"><mn>360</mn><mi>°</mi></mstyle></math> , and coterminal with <math><mstyle displaystyle="true"><mn>360</mn><mo>+</mo><mn>60</mn><mo>+</mo><mn>180</mn></mstyle></math> .

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mn>360</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>360</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> to <math><mstyle displaystyle="true"><mo>-</mo><mn>60</mn></mstyle></math> to find the positive angle.

Subtract <math><mstyle displaystyle="true"><mn>60</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> .

List the new angles.

The period of the <math><mstyle displaystyle="true"><mi>csc</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> degrees in both directions.

Do you know how to Solve for θ in Degrees csc(theta)=-(2 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 | seven hundred eighty-seven million two hundred forty-one thousand five hundred thirty-four |
---|

- 787241534 has 8 divisors, whose sum is
**1182166968** - The reverse of 787241534 is
**435142787** - Previous prime number is
**907**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 41
- Digital Root 5

Name | one billion one hundred thirteen million one hundred four thousand seven hundred ten |
---|

- 1113104710 has 16 divisors, whose sum is
**2005256736** - The reverse of 1113104710 is
**0174013111** - Previous prime number is
**1217**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 19
- Digital Root 1

Name | one billion two million five hundred fourteen thousand seven hundred eleven |
---|

- 1002514711 has 16 divisors, whose sum is
**1104048000** - The reverse of 1002514711 is
**1174152001** - Previous prime number is
**373**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 22
- Digital Root 4