Arcsec Calculator (Inverse Secant)


Degrees:


Radians:

π radians:

The domain of x is x≤-1 and x≥1.

The range is 0≤y< π/2 and π/2<y≤π.

Graph of arcsec (inverse secant)

With this calculator, you can get the result of the inverse secant of an input value. The solution will be displayed in degrees, radians, and π radians. The allowed domain of x is x≤-1 and x≥1.

Below you will find useful information on how to use the inverse secant calculator. In addition, you will also be able to learn about the definition, graph and common values of the inverse secant.

How to use the inverse secant calculator?

Passo 1: The value of x must be entered in the first input box. You must use a value of x in the domain x≤-1 and x≥1.

Passo 2: The angle in degrees will be displayed in the input box to the right.

Passo 3: Additional solutions in radians and π radians will be displayed at the bottom.

Difference between results displayed in degrees, radians, and π radians

We can find the relationship between degrees and radians by recalling that a complete circle has a total of 360° or 2π radians. Therefore, we can deduce that 180° is equal to π radians.

Also, the only difference between the result in “radians” and “π radians” is that “radians” already has the value of π included. For example, 0.5 π radians is equivalent to 1.571 radians since the value of π is approximately 3.1415.

What is inverse secant?

Inverse secant, also known as arc secant, is the inverse function of secant. Therefore, we can think of the inverse secant as a function that reverses the effect of the secant function.

For example, the secant of 60° is equal to 2. So the inverse secant of 2 is equal to 60°.

We can denote the inverse secant function as sec-1(x) or also as arcsec(x). Since the secant function and the cosine function are reciprocals, sec-1(x) is equivalent to cos-1(1/x).

The inverse secant can be used to determine an angle if we know the sides or the ratios of the sides of a right triangle. For example, angle A in the following triangle can be found using arcsec(x), where x equals c/b.

diagram-of-a-right-triangle-with-sides

Why can’t the inverse secant take values of x between -1 and 1?

The inverse secant is the inverse function of the secant. This means that their domains and ranges are swapped. That is, the range of the secant is the domain of the inverse secant.

There is no input value that causes the values of secant to be between -1 and 1. Therefore, the x values of the inverse secant cannot be between -1 and 1 either.

Inverse secant graph

The inverse secant can be plotted using a fixed range. In this calculator, the inverse secant takes any value of x, excluding numbers between -1 and 1, while the range is limited from 0 to π and not including π/2.

Graph of arcsec (inverse secant)

Inverse secant domain

Using the graph of the inverse secant, we can see that the values of x can be any real value, excluding values between -1 and 1. Therefore, the domain of the inverse secant is equal to x≤-1 and x≥1.

Inverse secant range

Using the graph of the inverse secant, we can see that the output values of the function range from 0 to π not including π/2. Therefore, its range is 0≤y<π/2 or π/2<y≤π.

Inverse secant table of common values

Value of xarcsec(x)(°)arcsec(x)(rad)
260°\frac{\pi}{3}
\sqrt{2}45°\frac{\pi}{4}
\frac{2\sqrt{3}}{3}30°\frac{\pi}{6}
10
-1180°π

Related calculators:

You can explore other calculators here.