The angle <math><mstyle displaystyle="true"><mn>45</mn></mstyle></math> is an angle where the values of the six trigonometric functions are known. Because this is the case, add <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> to keep the value the same.

Use the sum formula for cosine to simplify the expression. The formula states that <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo>)</mo></mrow><mo>=</mo><mo>-</mo><mrow><mo>(</mo><mi>cos</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow><mo>+</mo><mi>sin</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mi>sin</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mn>45</mn><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><mn>0</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mn>45</mn><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> .

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Add <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"><mn>0</mn></mstyle></math> .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

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Name | eighty-one million six hundred twenty-four thousand four hundred ninety-five |
---|

- 81624495 has 8 divisors, whose sum is
**130599216** - The reverse of 81624495 is
**59442618** - Previous prime number is
**5**

- Is Prime? no
- Number parity odd
- Number length 8
- Sum of Digits 39
- Digital Root 3

Name | one billion six hundred fifty-three million three hundred sixty-two thousand two hundred thirty |
---|

- 1653362230 has 16 divisors, whose sum is
**3204979344** - The reverse of 1653362230 is
**0322633561** - Previous prime number is
**13**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 31
- Digital Root 4

Name | four hundred forty-eight million eight hundred forty-eight thousand eight hundred twenty-two |
---|

- 448848822 has 32 divisors, whose sum is
**912100320** - The reverse of 448848822 is
**228848844** - Previous prime number is
**569**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 48
- Digital Root 3