To find the **cot inverse (arccot) of a value**, subtract the arctangent of the value from $\pi/2$. This formula helps determine the angle whose cotangent equals the given value.

The **Cot Inverse Calculator** is a handy tool for finding the arccotangent, or inverse cotangent, of a number. This calculation is common in trigonometry when you need to find an angle based on a cotangent value. Basically, the cot inverse function is used to determine the angle whose cotangent equals a specific value.

This tool is especially helpful in solving trigonometric equations and analyzing periodic functions. Moreover, this calculator provides the result in radians, making it valuable for fields like physics, engineering, and math where angle measurements are often needed.

**Formula:**

`$\text{arccot}(x) = \frac{\pi}{2} - \arctan(x)$`

Variable | Description |
---|---|

$\text{arccot}(x)$ | Inverse Cotangent (angle in radians) |

$x$ | Input value for which you want to find the arccot |

$\pi$ | Pi constant (approximately 3.14159) |

$\arctan(x)$ | Arctangent of $x$ |

**Solved Calculations:**

**Example 1:**

Calculate the cot inverse of $x = 1$.

Step | Calculation |
---|---|

1. | $\text{arccot}(1) = \frac{\pi}{2} – \arctan(1)$ |

2. | Since $\arctan(1) = \frac{\pi}{4}$ |

3. | $\text{arccot}(1) = \frac{\pi}{2} – \frac{\pi}{4}$ |

4. | $\text{arccot}(1) = \frac{\pi}{4}$ |

**Answer: $\frac{\pi}{4}$ radians**

**Example 2:**

Calculate the cot inverse of $x = \sqrt{3}$.

Step | Calculation |
---|---|

1. | $\text{arccot}(\sqrt{3}) = \frac{\pi}{2} – \arctan(\sqrt{3})$ |

2. | Since $\arctan(\sqrt{3}) = \frac{\pi}{3}$ |

3. | $\text{arccot}(\sqrt{3}) = \frac{\pi}{2} – \frac{\pi}{3}$ |

4. | $\text{arccot}(\sqrt{3}) = \frac{\pi}{6}$ |

**Answer: $\frac{\pi}{6}$ radians**