Draw a triangle in the plane with vertices <math><mstyle displaystyle="true"><mrow><mo>(</mo><mfrac><mrow><mn>12</mn></mrow><mrow><mn>13</mn></mrow></mfrac><mo>,</mo><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mfrac><mrow><mn>12</mn></mrow><mrow><mn>13</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt><mo>)</mo></mrow></mstyle></math> , <math><mstyle displaystyle="true"><mrow><mo>(</mo><mfrac><mrow><mn>12</mn></mrow><mrow><mn>13</mn></mrow></mfrac><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> , and the origin. Then <math><mstyle displaystyle="true"><mi>arccos</mi><mrow><mo>(</mo><mfrac><mrow><mn>12</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><mfrac><mrow><mn>12</mn></mrow><mrow><mn>13</mn></mrow></mfrac><mo>,</mo><msqrt><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mo>(</mo><mfrac><mrow><mn>12</mn></mrow><mrow><mn>13</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt><mo>)</mo></mrow></mstyle></math> . Therefore, <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>arccos</mi><mrow><mo>(</mo><mfrac><mrow><mn>12</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>12</mn></mrow><mrow><mn>13</mn></mrow></mfrac><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></msqrt></mrow><mrow><mfrac><mrow><mn>12</mn></mrow><mrow><mn>13</mn></mrow></mfrac></mrow></mfrac></mstyle></math> .

Multiply the numerator by the reciprocal of the denominator.

One to any power is one.

Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mn>12</mn></mrow><mrow><mn>13</mn></mrow></mfrac></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>12</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>144</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>169</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mfrac><mrow><mn>25</mn></mrow><mrow><mn>169</mn></mrow></mfrac></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>25</mn></msqrt></mrow><mrow><msqrt><mn>169</mn></msqrt></mrow></mfrac></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>5</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.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>13</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Combine <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>12</mn></mrow></mfrac></mstyle></math> .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Do you know how to Find the Exact Value tan(arccos(12/13))? 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 | one billion six hundred sixty-three million one hundred sixty-three thousand two hundred eighty-three |
---|

- 1663163283 has 16 divisors, whose sum is
**2278666656** - The reverse of 1663163283 is
**3823613661** - Previous prime number is
**4241**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 39
- Digital Root 3

Name | one billion eight hundred fifty-seven million three hundred eighteen thousand three hundred fifty-two |
---|

- 1857318352 has 32 divisors, whose sum is
**9402674238** - The reverse of 1857318352 is
**2538137581** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 43
- Digital Root 7

Name | one billion five hundred ninety-one million nine hundred sixty-one thousand eight hundred twenty-three |
---|

- 1591961823 has 8 divisors, whose sum is
**2358462000** - The reverse of 1591961823 is
**3281691951** - Previous prime number is
**3**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 45
- Digital Root 9