Apply the sine double-angle identity.

Factor <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> out of <math><mstyle displaystyle="true"><msqrt><mn>3</mn></msqrt><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> out of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mrow><mo>(</mo><mn>2</mn><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>+</mo><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><msqrt><mn>3</mn></msqrt></mstyle></math> .

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 <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Solve <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> .

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

Simplify the right side.

The exact value of <math><mstyle displaystyle="true"><mi>arccos</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> to find the solution in the fourth quadrant.

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></mstyle></math> .

To write <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></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> .

Combine fractions.

Combine <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></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> .

Find the period of <math><mstyle displaystyle="true"><mi>cos</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>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.

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>cos</mi><mrow><mo>(</mo><mi>θ</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 <math><mstyle displaystyle="true"><mn>2</mn><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>+</mo><msqrt><mn>3</mn></msqrt></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Solve <math><mstyle displaystyle="true"><mn>2</mn><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>=</mo><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><msqrt><mn>3</mn></msqrt></mstyle></math> from both sides of the equation.

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

Divide each term in <math><mstyle displaystyle="true"><mn>2</mn><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>=</mo><mo>-</mo><msqrt><mn>3</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><mi>θ</mi><mo>)</mo></mrow></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Move the negative in front of the fraction.

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><mfrac><mrow><mi>π</mi></mrow><mrow><mn>3</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.

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> .

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>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.

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>3</mn></mrow></mfrac></mstyle></math> to find the positive angle.

To write <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></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> .

Combine fractions.

Combine <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>3</mn></mrow></mfrac></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><mi>θ</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"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mrow><mo>(</mo><mn>2</mn><mi>sin</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> true.

Consolidate <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mn>2</mn><mi>π</mi><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mn>2</mn><mi>π</mi><mi>n</mi></mstyle></math> to <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mi>π</mi><mi>n</mi></mstyle></math> .

Do you know how to Solve for θ in Radians sin(2theta)+ square root of 3cos(theta)=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 | seven hundred twenty million four hundred seventy-nine thousand five hundred twenty-two |
---|

- 720479522 has 16 divisors, whose sum is
**1235656512** - The reverse of 720479522 is
**225974027** - Previous prime number is
**20333**

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

Name | one billion six million eight hundred four thousand three hundred eighty-four |
---|

- 1006804384 has 128 divisors, whose sum is
**7657182720** - The reverse of 1006804384 is
**4834086001** - Previous prime number is
**659**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 34
- Digital Root 7

Name | three million nine hundred fifty-five thousand four hundred seventy-six |
---|

- 3955476 has 32 divisors, whose sum is
**9492480** - The reverse of 3955476 is
**6745593** - Previous prime number is
**31**

- Is Prime? no
- Number parity even
- Number length 7
- Sum of Digits 39
- Digital Root 3