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 | three hundred ninety million four hundred twenty-four thousand ninety-one |
---|

- 390424091 has 4 divisors, whose sum is
**413390232** - The reverse of 390424091 is
**190424093** - Previous prime number is
**17**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 32
- Digital Root 5

Name | five hundred ninety-six million nine hundred eighty-two thousand two hundred sixteen |
---|

- 596982216 has 64 divisors, whose sum is
**2696900832** - The reverse of 596982216 is
**612289695** - Previous prime number is
**257**

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

Name | one billion eight hundred fifty-five million two hundred sixty-three thousand one hundred ninety-seven |
---|

- 1855263197 has 4 divisors, whose sum is
**1919237820** - The reverse of 1855263197 is
**7913625581** - Previous prime number is
**29**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 47
- Digital Root 2