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

The exact value of <math><mstyle displaystyle="true"><mi>arcsin</mi><mrow><mo>(</mo><mo>-</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mn>3</mn><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></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>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

The sine function is negative in the third and fourth quadrants. To find the second solution, subtract the solution from <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> , to find a reference angle. Next, add this reference angle to <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> to find the solution in the third quadrant.

Subtract <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> from <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi><mo>+</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac><mo>+</mo><mi>π</mi></mstyle></math> .

The resulting angle of <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> is positive, less than <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> , and coterminal with <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi><mo>+</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac><mo>+</mo><mi>π</mi></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mn>3</mn><mi>x</mi><mo>=</mo><mfrac><mrow><mn>4</mn><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>3</mn><mi>x</mi><mo>=</mo><mfrac><mrow><mn>4</mn><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></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>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mi>π</mi></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>3</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>3</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> to <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>9</mn></mrow></mfrac></mstyle></math> to find the positive angle.

To write <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

Write each expression with a common denominator of <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> , by multiplying each by an appropriate factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> from <math><mstyle displaystyle="true"><mn>6</mn><mi>π</mi></mstyle></math> .

List the new angles.

The period of the <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mn>3</mn><mi>x</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> radians in both directions.

Do you know how to Solve for x in Radians sin(3x)=-( square root of 3)/2? 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 hundred nine million four hundred forty-two thousand one hundred thirty |
---|

- 109442130 has 16 divisors, whose sum is
**200123136** - The reverse of 109442130 is
**031244901** - Previous prime number is
**7**

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

Name | five hundred seventy-eight million one hundred sixty-nine thousand six hundred eighty |
---|

- 578169680 has 256 divisors, whose sum is
**3849120000** - The reverse of 578169680 is
**086961875** - Previous prime number is
**239**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 50
- Digital Root 5

Name | one billion five hundred thirty-nine million five hundred fifty-one thousand nine hundred thirty-seven |
---|

- 1539551937 has 32 divisors, whose sum is
**2563799040** - The reverse of 1539551937 is
**7391559351** - Previous prime number is
**593**

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