Let <math><mstyle displaystyle="true"><mi>u</mi><mo>=</mo><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> . Substitute <math><mstyle displaystyle="true"><mi>u</mi></mstyle></math> for all occurrences of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Factor by grouping.

For a polynomial of the form <math><mstyle displaystyle="true"><mi>a</mi><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></mstyle></math> , rewrite the middle term as a sum of two terms whose product is <math><mstyle displaystyle="true"><mi>a</mi><mo>⋅</mo><mi>c</mi><mo>=</mo><mn>3</mn><mo>⋅</mo><mo>-</mo><mn>2</mn><mo>=</mo><mo>-</mo><mn>6</mn></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mn>1</mn></mstyle></math> .

Multiply by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> plus <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math>

Apply the distributive property.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

Factor out the greatest common factor (GCF) from each group.

Factor the polynomial by factoring out the greatest common factor, <math><mstyle displaystyle="true"><mn>3</mn><mi>u</mi><mo>-</mo><mn>2</mn></mstyle></math> .

Replace all occurrences of <math><mstyle displaystyle="true"><mi>u</mi></mstyle></math> with <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> .

Replace the left side with the factored expression.

If any individual factor on the left side of the equation is equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , the entire expression will be equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Set the first factor equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to both sides of the equation.

Divide each term by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> and simplify.

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

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

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><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.

Evaluate <math><mstyle displaystyle="true"><mi>arcsin</mi><mrow><mo>(</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo>)</mo></mrow></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.

Simplify the expression to find the second solution.

Remove the parentheses around the expression <math><mstyle displaystyle="true"><mn>3.14159265</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>0.72972765</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>3.14159265</mn></mstyle></math> .

Find the period.

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>1</mn></mstyle></math> in the formula for period.

Solve the equation.

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>2</mn><mi>π</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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

Set the next factor equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> from both sides of the equation.

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><mn>1</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></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.

Simplify the expression to find the second solution.

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

To write <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mn>1</mn></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Write each expression with a common denominator of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> , by multiplying each by an appropriate factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

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

Add <math><mstyle displaystyle="true"><mn>4</mn><mi>π</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

To write <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>1</mn></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Write each expression with a common denominator of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> , by multiplying each by an appropriate factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Move <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>5</mn><mi>π</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> from <math><mstyle displaystyle="true"><mfrac><mrow><mn>7</mn><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

The resulting angle of <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mrow><mn>2</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"><mfrac><mrow><mn>7</mn><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Find the period.

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>1</mn></mstyle></math> in the formula for period.

Solve the equation.

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>2</mn><mi>π</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> to every negative angle to get positive angles.

Add <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> to <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</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>1</mn></mrow></mfrac></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Write each expression with a common denominator of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> , by multiplying each by an appropriate factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply <math><mstyle displaystyle="true"><mn>2</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>4</mn><mi>π</mi></mstyle></math> .

List the new angles.

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

The final solution is all the values that make <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>3</mn><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>-</mo><mn>2</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> true.

Do you know how to Solve for x 3sin(x)^2+sin(x)-2=0? 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 | nine hundred four million three hundred eighty-three thousand seven hundred thirty-one |
---|

- 904383731 has 4 divisors, whose sum is
**957582792** - The reverse of 904383731 is
**137383409** - Previous prime number is
**17**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 38
- Digital Root 2

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

- 2104229702 has 4 divisors, whose sum is
**3156344556** - The reverse of 2104229702 is
**2079224012** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 29
- Digital Root 2

Name | seven hundred four million two hundred two thousand nine hundred forty |
---|

- 704202940 has 64 divisors, whose sum is
**2175916608** - The reverse of 704202940 is
**049202407** - Previous prime number is
**841**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 28
- Digital Root 1