Divide each term in <math><mstyle displaystyle="true"><mn>2</mn><mi>sin</mi><mrow><mo>(</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msqrt><mn>2</mn></msqrt></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac><mi>x</mi><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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.

Combine <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>arcsin</mi><mrow><mo>(</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Multiply both sides of the equation by <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math> .

Simplify the left side.

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mi>π</mi></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mi>π</mi><mi>x</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

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

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mi>π</mi><mi>x</mi></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Simplify the right side.

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

Cancel the common factor of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Combine <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> to find the solution in the second quadrant.

Multiply both sides of the equation by <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math> .

Simplify both sides of the equation.

Simplify the left side.

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mi>π</mi></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mi>π</mi><mi>x</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> .

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

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mi>π</mi><mi>x</mi></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Simplify the right side.

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mi>π</mi></mrow></mfrac><mrow><mo>(</mo><mi>π</mi><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

To write <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Combine fractions.

Combine <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Move <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> from <math><mstyle displaystyle="true"><mn>4</mn><mi>π</mi></mstyle></math> .

Simplify terms.

Cancel the common factor of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mn>3</mn><mi>π</mi></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Combine <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</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"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> in the formula for period.

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

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

The period of the <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac><mi>x</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> radians in both directions.

Do you know how to Solve for x in Radians 2sin(pi/3x) = square root of 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 | four hundred fifty-nine million six hundred sixty-one thousand seven hundred thirty-four |
---|

- 459661734 has 16 divisors, whose sum is
**701256960** - The reverse of 459661734 is
**437166954** - Previous prime number is
**1181**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 45
- Digital Root 9

Name | one billion five hundred twenty-four million five hundred thirty-two thousand nine hundred thirty-four |
---|

- 1524532934 has 4 divisors, whose sum is
**2286799404** - The reverse of 1524532934 is
**4392354251** - Previous prime number is
**2**

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

Name | one billion twenty-five million five hundred forty-four thousand five hundred four |
---|

- 1025544504 has 128 divisors, whose sum is
**4710182400** - The reverse of 1025544504 is
**4054455201** - Previous prime number is
**131**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 30
- Digital Root 3