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><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> .

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.

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>4</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Write each expression with a common denominator of <math><mstyle displaystyle="true"><mn>4</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>4</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>4</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>8</mn><mi>π</mi></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.

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>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.

Do you know how to Solve for ? cos(theta)=( square root of 2)/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 | one billion two hundred forty-five million three hundred eighty-seven thousand seven |
---|

- 1245387007 has 4 divisors, whose sum is
**1245458880** - The reverse of 1245387007 is
**7007835421** - Previous prime number is
**42719**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 37
- Digital Root 1

Name | five hundred thirty-nine million seven hundred seventeen thousand nine hundred forty-one |
---|

- 539717941 has 8 divisors, whose sum is
**620906624** - The reverse of 539717941 is
**149717935** - Previous prime number is
**151**

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

Name | four hundred thirty-one million six hundred forty-nine thousand seven hundred seventy-two |
---|

- 431649772 has 8 divisors, whose sum is
**971211996** - The reverse of 431649772 is
**277946134** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 43
- Digital Root 7