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(θ) = 1/cos(θ).
What is the angle θ?
The Greek letter theta (θ) 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 π/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 2π radians. Half a circle would be π radians (half of 2π). A quarter circle is 2π/4 = π/2 radians. An eighth of a circle is 2π/8 = π/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.
a2 + b2 = c2
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:
√(52 + 22) = √(25 + 4) = √29
The hypotenuse is √29
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 π/2 | (-∞, ∞) |
| sec(x) | All real numbers except multiples of π | (1, ∞) U (-∞, -1) |
| csc(x) | All real numbers except integer multiples of π | (-∞, -1) U (1, ∞) |
| cot(x) | All real numbers except integer multiples of π | (-∞, ∞) |
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 73 functions in the 'Math and trigonometry' category.
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