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.

The exact value of <math><mstyle displaystyle="true"><mi>arccos</mi><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

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

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>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Combine <math><mstyle displaystyle="true"><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.

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

Divide each term in <math><mstyle displaystyle="true"><mn>2</mn><mi>θ</mi><mo>=</mo><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></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>θ</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>3</mn><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

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

The cosine function is negative in the second and third 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 third quadrant.

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

Move all terms not containing <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> to the right side of the equation.

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

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>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Combine <math><mstyle displaystyle="true"><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.

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

Divide each term in <math><mstyle displaystyle="true"><mn>2</mn><mi>θ</mi><mo>=</mo><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></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>θ</mi><mo>=</mo><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></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>θ</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>3</mn><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

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

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

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><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><mn>2</mn><mi>θ</mi><mo>-</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> radians in both directions.

Do you know how to Solve for θ in Radians cos(2theta-pi/2)=-1? 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 billion eight hundred forty-eight million five hundred thirteen thousand two hundred forty-seven |
---|

- 1848513247 has 16 divisors, whose sum is
**2150853120** - The reverse of 1848513247 is
**7423158481** - Previous prime number is
**1117**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 43
- Digital Root 7

Name | six hundred sixty-seven million three hundred thirty-two thousand two hundred eighteen |
---|

- 667332218 has 8 divisors, whose sum is
**1143998112** - The reverse of 667332218 is
**812233766** - Previous prime number is
**7**

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

Name | five hundred fifty-seven million nine hundred six thousand six hundred seventeen |
---|

- 557906617 has 8 divisors, whose sum is
**563439240** - The reverse of 557906617 is
**716609755** - Previous prime number is
**181**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 46
- Digital Root 1