Secant Calculator (Degrees and Radians)

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Graph of secant

With this calculator, you can get the secant of any entered angle. It is possible to use degrees, radians, and π radians. The secant of the entered angle will be displayed immediately.

Below is more information on how to use the Secant Calculator. In addition, you will be able to learn about secant in general. You will learn about its definition, its graph, and the values of the secant of important angles.

How to use the secant calculator?

Step 1: Start by selecting the type of angle you want to use. By clicking the blue button, you can select between using degrees, radians, or π radians.

Step 2: Enter the angle in the “Angle” input box. Any positive or negative angle can be used.

Step 3: The secant of the entered angle will be displayed in the right panel. If this is the case, it will be indicated if the secant is undefined.

What is the difference between degrees, radians, and π radians on the calculator?

The equivalence between degrees and radians can be found by recalling that a complete circle is equal to 360° or equal to 2π radians. This means that 180° is equal to π radians.

Now, the difference between radians and π radians is simply that π radians multiplies by π whatever value is entered. That is, remembering that the constant π has an approximate value of 3.1415…, π radians is equal to 3.1415 radians.

Therefore, if we want to enter 0.25π, select the “π radians” option and simply enter 0.25.

This means that, if we want to find the secant of the 45° angle, we can use the following equivalent options:

We can select “degrees” and enter 45.
We can select “π radians” and enter 0.25 (45° equals 1/4 π radians).
We can select “radians” and enter 0.7854 (0.25π radians equals 0.7854 radians).

What is the secant of an angle?

The secant of an angle is the reciprocal function of the cosine of an angle. That is, the secant can be defined as 1 over the cosine of the angle.

Additionally, we can define the secant of an angle using a right triangle. Therefore, the secant of an angle is equal to the hypotenuse on the adjacent side.

For example, in the following right triangle, the secant of angle A can be defined as the length of side c (hypotenuse) divided by the length of side b (side adjacent to A).

Similarly, the secant of angle B can be defined as the length of side c (hypotenuse) divided by the length of side a (side adjacent to B).

If you want to learn more about the secant of an angle, you can visit our article Secant of an Angle – Formulas and Examples .

Why is the secant of 90° and 270° undefined?

Due to the definition of secant, we can see that by using the angles 90° and 270° in the calculator, we get “Undefined”.

The secant of 90° and 270° are undefined because the secant can be defined as 1 over the cosine of the angle. This means that all the angles that result in cosine equal to zero, have an undefined secant.

The cosine is equal to 0 when the angle is equal to 90°. Also, due to the periodicity of the cosine function, the value repeats every time we add 180°n, where n is a positive or negative integer.

For example, the cosine of 90°+180°=270°, is also equal to 0, so the secant is undefined.

Graph of the secant of an angle

Although the secant of an angle is primarily defined using a right triangle, we can use any angle, both positive and negative, to form its graph.

The secant function is periodic. This means that the graph repeats itself after a constant interval. The period of the secant function is equal to 360° or 2π.

Domain of the secant of an angle

In the graph of the secant, we can see that the secant can take both positive and negative values. Also, the values extend to both positive and negative infinity.

However, the secant function forms asymptotes at some values. That is, we can’t use some values, since the function becomes undefined there. The values that we cannot use are equal to 90°+180°n, where n is a positive and negative integer.

Therefore, the domain of the secant function is equal to all real numbers except 90°+180°n or ½π+πn.

Range of the secant of an angle

Using the graph of secant, we can see that the function has output values that are both positive and negative. However, the function excludes values from -1 to 1.

Therefore, the range of secant is equal to all real numbers, excluding values from -1 to 1, but -1 and 1 are included.

Secant table of common angles

Degrees	Radians	Secant
90°	$\frac{\pi}{2}$	Undefined
60°	$\frac{\pi}{3}$
45°	$\frac{\pi}{4}$	$\sqrt{2}$
30°	$\frac{\pi}{6}$	$\frac{2\sqrt{3}}{3}$
0°	0	1