Secant

Do you need calculate the secant online? Below you have a calculator to obtain the value of this trigonometric function from the angle, either in degrees or radians.

Just type the value of the angle for which you want to obtain the secant, select whether it is in degrees or radians and press the calculate button to obtain the result.



Secant formula

Triangle to calculate trigonometric ratios

We can calculate the secant of an angle by dividing the value of the hypotenuse by the adjoining leg.

If you are familiar with trigonometric ratios, you will have noticed that the secant is the inverse of cosine. Therefore, we can also compute the inverse of the cosine as we can see in the following formula:

Drying formula

Table of secant function values

To have a more global vision of the values of the secant of an angle, here is a table with the values of the secant of an angle. most typical angle values:

GradesRadiansSecant
01
30ºπ/61,1547
45ºπ/41,4144
60ºπ/32
90ºπ/2±∞
180ºπ-1,0152
270º3π/2±∞
315º7π/41,4144
360º1

Values of the secant according to quadrants

In addition, its value will be positive or negative depending on the quadrant in which we are located:

  • First and fourth quadrants: the secant will be greater than 1
  • Second and third quadrant: will be less than 1

If we plot the values in the table above, we can see what it looks like if we plot it graphically and reveal that it is a periodic function every 2π radians or 360º.

Secant graph

Characteristics of the blotter

Now that we know that the secant is a periodic function, let's see what the rest of its characteristics are:

  • Domain: ℝ, except for values that are multiples of (π/2 + aπ). At these values, the function tends to ±∞
  • The range is in the interval (-∞, -1] U (1, +∞)

Derivative of the secant

The derivative of the secant of x is equal to the secant of x times the tangent of x . This can be represented by the following formula:

f(x) = secx → f'(x) = secx - tanx

If instead of x, we have to calculate the derivative of the secant of a functionthen it will be like this:

f(u) = secu → f'(u) = u' secu - tanu

The only added difficulty in deriving the secant of a function is to also add the derivative of the function itself to the result.

Integral of the secant

If what we want is calculate the secant integral, below you have the formula:

Integral of the secant

As you can see, it is equal to the neperian logarithm of the absolute value of the secant of x + the tangent of x.

How to calculate the secant in Excel

Calculate secant in Excel

If you want to finding the secant of an angle using ExcelYou can do this very easily by typing one of the following functions in an empty cell:

If the angle is in degrees:

=SEC(RADIANS(angle))

We only have to replace the word "angle" with the degrees we want. For example, if we want to calculate the 30 degree blotterwe will write the function as follows:

=SEC(RADIANS(30))

If the angle is expressed in radians, the formula to use in Excel will be the following:

=SEC()

In this case, we will write the number of radians between the parentheses. For example, if we want to know what is the secant of 0we will write it like this:

=SEC(0)

Secant as a function of other trigonometric ratios

Since all the trigonometric ratios are related to each other, we can express the secant as a function of sine, cosine, or any other. Below are the formulas to be used in each case:

Depending on the sine::

Secant as a function of sine

Depending on the cosine:

Secant as a function of cosine

Depending on the tangent:

Secant as a function of tangent

Depending on the cosecant:

Secant as a function of cosecant

Depending on the cotangent:

Secant as a function of cotangent

All formulas that have a (1) to the right mean that the result can be positive or negative depending on the quadrant in which the angle is located.

Calculate secant in scientific calculator

Online secant calculator

Scientific calculators usually do not have a dedicated key to calculate the secant, so we will do the process in two parts.

To see it in a simpler way, we will do it directly with an example in which we are going to calculate the secant of 60 degrees.

The first step consists of calculate the cosine of that angle. To do this, press the following key combination:

COS > 60 > =

With the result on the screen, then press the key with x-1 and press the equals (=). Here what we are doing is calculating the inverse of the cosine we have obtained (remember that sec (x) = 1/cos(x)).

If you have done it right, you will see 1.1547 on the display, which is precisely the 60 degree desiccant.

We can also do the calculation in radians, but to do so, we will have to enter the configuration mode of our calculator and change the "degrees" to "rads".

If you want to avoid this whole process, the easiest and most convenient way is to use our online secant calculator and thus avoid any type of problem or error in the calculations.

If you have any doubts about this trigonometric function and how to calculate it, leave us a comment and we will help you to clear all your doubts.

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