# How to use the SEC function

**What is the SEC function?**

The SEC function calculates the secant of an angle.

**What is a secant?**

The trigonometric secant is a function that defines an angle of a right-angled triangle to the ratio of the hypotenuse to the adjacent side. It is also the inverse of the cosine, sec(Î¸) = 1/cos(Î¸).

**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 right triangle?**

A right triangle is a type of triangle that contains one internal angle measuring 90 degrees or Ï€/2 radians (a right angle).

**What are radians?**

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 is the Pythagorean theorem?**

The Pythagorean theorem is a mathematical relationship between the sides of a right triangle. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

a^{2} + b^{2} = c^{2}

a and b are the lengths of the legs of the triangle

c is the length of the hypotenuse

For example, in a triangle with legs 5 and 2:

âˆš(5^{2} + 2^{2)} = âˆš(25 + 4) = âˆš29

The hypotenuse is âˆš29

**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) |

Formula in cell E3:

### Excel Function Syntax

SEC(*number*)

### Arguments

number |
Required. The number (radians) for which you want to calculate the secant. |

The secant is calculated like this:

### Functions in 'Math and trigonometry' category

The SEC function function is one of 63 functions in the 'Math and trigonometry' category.

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