# How to use the TAN function

**What is the TAN function?**

The TAN function calculates the tangent of an angle in radians.

**What is the trigonometric tangent?**

The tan is a trigonometric function that relates an angle Î¸ in a right triangle to the ratio of the side lengths of a right triangle.

tan(Î¸) = opposite / adjacent

**What is a right triangle?**

A right triangle must have one angle that measures exactly 90Â° or Ï€/2 radians which is approximately 1.5707963267949 radians.

**What is the angle Î¸?**

The Greek letter theta (Î¸) is commonly used to represent an unknown angle in a right triangle.

**What is a radian?**

Radians are a unit used to measure angles. An angle of 1 radian has an arc length equal to the circle's radius

**What is the relationship between the number pi and radians?**

Radians measure angles by the length of the arc they make in a circle rather than degrees. The full circumference of any circle is 2Ï€ multiplied by the circle's radius (2Ï€r).

Since the circumference goes all the way around a circle, that means the full circle measures 2Ï€ radians. Half a circle would be Ï€ radians (half of 2Ï€). A quarter circle is 2Ï€/4 = Ï€/2 radians. An eighth of a circle is 2Ï€/8 = Ï€/4 radians.

Excel has a function that returns the number pi:Â PI function

**What is an arc?**

An arc is a curved segment of a circle's circumference, it is a portion of the circle's curve, defined by two endpoints.

In other words, an arc is formed by two radii intersecting the circumference and the enclosed edge between them.

**What is a circle's radius?**

The radius of a circle is the distance from the center point to any point on the circle's edge or circumference.

**What is radii?**

The plural form of the word "radius".

**What is the radius of a circle?**

The radius of a circle is the distance from the center point to any point on the circle's edge or circumference.

**What are the main trigonometric functions?**

Function |
Domain (input) |
Range (output) |

sin(x) | All real numbers | (-1, 1) |

cos(x) | All real numbers | (-1, 1) |

tan(x) | All real numbers except multiples of Ï€/2 | (-âˆž, âˆž) |

sec(x) | All real numbers except multiples of Ï€ | (1, âˆž) U (-âˆž, -1) |

csc(x) | All real numbers except integer multiples of Ï€ | (-âˆž, -1) U (1, âˆž) |

cot(x) | All real numbers except integer multiples of Ï€ | (-âˆž, âˆž) |

### TAN function Syntax

TAN(*number*)

### TAN functionArguments

number |
Required. The radian angle you want to know the tangent of. |

### TAN function example

Formula in cell C3:

Use the RADIANS function to convert degrees to radians.

### Functions in 'Math and trigonometry' category

The TAN function function is one of 69 functions in the 'Math and trigonometry' category.

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