Divide each term in <math><mstyle displaystyle="true"><mn>4</mn><msup><mi>sin</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>=</mo><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><msup><mi>sin</mi><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

Rewrite <math><mstyle displaystyle="true"><msqrt><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><msqrt><mn>4</mn></msqrt></mrow></mfrac></mstyle></math> .

Simplify the denominator.

Rewrite <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

First, use the positive value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the first solution.

Next, use the negative value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the second solution.

The complete solution is the result of both the positive and negative portions of the solution.

Set up each of the solutions to solve for <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> .

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

Simplify the right side.

The exact value of <math><mstyle displaystyle="true"><mi>arcsin</mi><mrow><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"><mn>60</mn></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"><mn>180</mn></mstyle></math> to find the solution in the second quadrant.

Subtract <math><mstyle displaystyle="true"><mn>60</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> .

Find the period of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></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> .

The period of the <math><mstyle displaystyle="true"><mi>sin</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.

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

Simplify the right side.

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><mn>60</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>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.

Simplify the expression to find the second solution.

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> .

Find the period of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></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 every negative angle to get positive angles.

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>sin</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.

List all of the solutions.

Consolidate <math><mstyle displaystyle="true"><mn>60</mn><mo>+</mo><mn>360</mn><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>240</mn><mo>+</mo><mn>360</mn><mi>n</mi></mstyle></math> to <math><mstyle displaystyle="true"><mn>60</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> .

Consolidate <math><mstyle displaystyle="true"><mn>120</mn><mo>+</mo><mn>360</mn><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>300</mn><mo>+</mo><mn>360</mn><mi>n</mi></mstyle></math> to <math><mstyle displaystyle="true"><mn>120</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> .

Do you know how to Solve for θ in Degrees 4sin(theta)^2=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 | three hundred eight million eight hundred ninety thousand forty |
---|

- 308890040 has 32 divisors, whose sum is
**1251004824** - The reverse of 308890040 is
**040098803** - Previous prime number is
**5**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 32
- Digital Root 5

Name | five hundred fifty-six million six hundred thirty-three thousand one hundred seventy-three |
---|

- 556633173 has 8 divisors, whose sum is
**757968768** - The reverse of 556633173 is
**371336655** - Previous prime number is
**47**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 39
- Digital Root 3

Name | one billion nine hundred ninety-five million one hundred forty-one thousand four hundred forty-three |
---|

- 1995141443 has 4 divisors, whose sum is
**1995355008** - The reverse of 1995141443 is
**3441415991** - Previous prime number is
**9791**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 41
- Digital Root 5