To convert radians to degrees, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>180</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math> , since a full circle is <math><mstyle displaystyle="true"><mn>360</mn><mi>°</mi></mstyle></math> or <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> radians.

Split <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>12</mn></mrow></mfrac></mstyle></math> into two angles where the values of the six trigonometric functions are known.

Apply the difference of angles identity <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>)</mo></mrow><mo>=</mo><mi>cos</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow><mo>+</mo><mi>sin</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>sin</mi><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>4</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>6</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Simplify each term.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

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

Combine using the product rule for radicals.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

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

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>2</mn></msqrt></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><msqrt><mn>2</mn></msqrt></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> .

Combine the numerators over the common denominator.

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

Factor <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Apply the distributive property.

Combine <math><mstyle displaystyle="true"><msqrt><mn>6</mn></msqrt></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>45</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math> .

Combine <math><mstyle displaystyle="true"><msqrt><mn>2</mn></msqrt></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>45</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math> .

Move <math><mstyle displaystyle="true"><mn>45</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><msqrt><mn>6</mn></msqrt></mstyle></math> .

Move <math><mstyle displaystyle="true"><mn>45</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><msqrt><mn>2</mn></msqrt></mstyle></math> .

Convert to a decimal.

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Name | six hundred seventy-nine million nine hundred six thousand four hundred ninety-four |
---|

- 679906494 has 32 divisors, whose sum is
**1518596640** - The reverse of 679906494 is
**494609976** - Previous prime number is
**197**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 54
- Digital Root 9

Name | three hundred eighty-seven million two hundred fifty-nine thousand seven hundred ninety-seven |
---|

- 387259797 has 16 divisors, whose sum is
**531625472** - The reverse of 387259797 is
**797952783** - Previous prime number is
**421**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 57
- Digital Root 3

Name | one billion eight hundred fifty-one million seven hundred sixty-six thousand three hundred eighty-nine |
---|

- 1851766389 has 16 divisors, whose sum is
**3297112000** - The reverse of 1851766389 is
**9836671581** - Previous prime number is
**3**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 54
- Digital Root 9