**π Part 1: Introduce**

**π Definition** The TAN function in Microsoft Excel returns the tangent of a given angle.

**π― Purpose** The function is primarily used to compute the tangent of an angle, which is a fundamental trigonometric function.

**π§ Syntax & Arguments**

`TAN(number)`

**Number**: The angle in radians for which you want the tangent.

**π Explain the Arguments in the function**

**Number**: This is a required argument. It represents the angle in radians for which the tangent needs to be calculated.

**π Return value** The function returns the tangent of the specified angle.

**π‘ Remarks** If your angle is in degrees, multiply it by PI()/180 or use the RADIANS function to convert it to radians.

**π Part 2: Examples**

**π’ Example 1: Calculating the Tangent of an Angle in Radians**

**π― Purpose**: To compute the tangent of an angle given in radians.**π Datasheet and formulas**:

A | B | C | |
---|---|---|---|

1 | Angle (Radians) | TAN Formula | Result |

2 | 0.785 | =TAN(A2) | 0.99920 |

**π Explanation**: This example demonstrates how to use the TAN function to calculate the tangent of an angle provided in radians. The result for an angle of 0.785 radians is approximately 0.99920.

**π’ Example 2: Tangent of an Angle in Degrees**

**π― Purpose**: To compute the tangent of an angle given in degrees.**π Datasheet and formulas**:

A | B | C | |
---|---|---|---|

1 | Angle (Degrees) | TAN Formula | Result |

2 | 45 | =TAN(RADIANS(A2)) | 1 |

**π Explanation**: This example demonstrates how to convert an angle from degrees to radians using the RADIANS function and then compute its tangent. The tangent of 45 degrees is 1.

**π’ Example 3: Using TAN with PI**

**π― Purpose**: To compute the tangent of half of Ο (equivalent to 90 degrees).**π Datasheet and formulas**:

A | B | C | |
---|---|---|---|

1 | Value | TAN Formula | Result |

2 | PI()/2 | =TAN(A2) | β |

**π Explanation**: Mathematics’s tangent of Ο/2 or 90 degrees is undefined (or infinity). In Excel, this will return a vast number.

**π’ Example 4: Negative Angle**

**π― Purpose**: To compute the tangent of a negative angle.**π Datasheet and formulas**:

A | B | C | |
---|---|---|---|

1 | Angle (Radians) | TAN Formula | Result |

2 | -0.785 | =TAN(A2) | -0.99920 |

**π Explanation**: The tangent function is periodic and odd, meaning TAN(-ΞΈ) = -TAN(ΞΈ). Thus, the tangent of -0.785 radians is approximately -0.99920.

**π’ Example 5: Tangent of Zero**

**π― Purpose**: To compute the tangent of zero.**π Datasheet and formulas**:

A | B | C | |
---|---|---|---|

1 | Angle (Radians) | TAN Formula | Result |

2 | 0 | =TAN(A2) | 0 |

**π Explanation**: The tangent of 0 radians (or 0 degrees) is 0. This is a fundamental property of the tangent function.

**π Part 3: Tips and tricks**

- π« Always ensure that the angle you provide to the TAN function is in radians.
- β Use the RADIANS function to easily convert degrees to radians before using them in the TAN function.
- π Regularly check for updates and additional functionalities Microsoft provides for the TAN function.
- β Consider using TAN in combination with other trigonometric functions to derive more meaningful insights from your data.