Draw a triangle in the plane with vertices <math><mstyle displaystyle="true"><mrow><mo>(</mo><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>13</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt><mo>,</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>13</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> , <math><mstyle displaystyle="true"><mrow><mo>(</mo><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>13</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> , and the origin. Then <math><mstyle displaystyle="true"><mi>arcsin</mi><mrow><mo>(</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>13</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is the angle between the positive x-axis and the ray beginning at the origin and passing through <math><mstyle displaystyle="true"><mrow><mo>(</mo><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>13</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt><mo>,</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>13</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> . Therefore, <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>arcsin</mi><mrow><mo>(</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>13</mn></mrow></mfrac><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>13</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt></mrow><mrow><mn>1</mn></mrow></mfrac></mstyle></math> .

Divide <math><mstyle displaystyle="true"><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>13</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

One to any power is one.

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn></mrow><mrow><mn>13</mn></mrow></mfrac></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

To write <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></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>169</mn></mrow><mrow><mn>169</mn></mrow></mfrac></mstyle></math> .

Combine.

Multiply <math><mstyle displaystyle="true"><mn>169</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine the numerators over the common denominator.

Multiply <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>169</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>169</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mfrac><mrow><mn>144</mn></mrow><mrow><mn>169</mn></mrow></mfrac></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>144</mn></msqrt></mrow><mrow><msqrt><mn>169</mn></msqrt></mrow></mfrac></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>144</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>12</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

Rewrite <math><mstyle displaystyle="true"><mn>169</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>13</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Do you know how to Simplify cos(arcsin(5/13))? 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 | five hundred ninety-six million eight hundred ninety-nine thousand two hundred seven |
---|

- 596899207 has 4 divisors, whose sum is
**613031656** - The reverse of 596899207 is
**702998695** - Previous prime number is
**37**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 55
- Digital Root 1

Name | one billion nine hundred nine million nine hundred sixty-seven thousand six hundred thirty-four |
---|

- 1909967634 has 32 divisors, whose sum is
**4246741440** - The reverse of 1909967634 is
**4367699091** - Previous prime number is
**17747**

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

Name | seventy-six million nine hundred fifty-eight thousand five hundred sixty-nine |
---|

- 76958569 has 4 divisors, whose sum is
**81009040** - The reverse of 76958569 is
**96585967** - Previous prime number is
**19**

- Is Prime? no
- Number parity odd
- Number length 8
- Sum of Digits 55
- Digital Root 1