Tangent Calculator (Degrees and Radians)


Answer:


Graph of tangent (radians and degrees)

This calculator allows you to find the tangent of any entered angle. You can use degrees, radians, and π radians. When entering an angle, the tangent will be displayed immediately.

Here is some additional information on how to use the tangent calculator. In addition, you will also be able to learn more about the tangent of an angle. You can learn the definition of tangent, its graph, and the tangent values of important angles.

How to use the tangent calculator?

Step 1: Select the type of angle to be used when clicking the blue button. You can select between using degrees, radians, or π radians.

Step 2: Enter the angle in the corresponding input box. You can use both positive and negative angles.

Step 3: The tangent of an angle will be displayed on the right panel. It will also be indicated if the tangent of an angle is undefined.

Using degrees, radians and π radians in the calculator

Remember that one complete revolution is equivalent to 360°. This is also equal to 2π radians. Therefore, we can deduce that 180° is equal to π radians.

Also, the constant π has a value of approximately 3.1415… This means that π radians is equal to approximately 3.1415 radians. Therefore, we can use these relationships to enter angles correctly.

For example, suppose we want to determine the tangent of the angle 60°. The following three forms are equivalent:

  • We can choose the “degrees” option and enter 60.
  • We can choose the “π radians” option and enter 0.3333 (180° equals π radians, so 60° equals 1/3 π radians).
  • We can choose the “radians” option and enter 1.0472 (0.3333π radians is equal to 1.0472 radians).

That is, the only difference between “π radians” and “radians” is that the “π radians” option multiplies the entered angle by π.

What is the tangent of an angle?

The tangent is one of the fundamental trigonometric functions. We can define the tangent with reference to a right triangle. So, the tangent is equal to the length of the opposite side divided by the length of the side adjacent to the angle.

In addition, the tangent of an angle can also be defined in terms of the sine and cosine of the angle. Therefore, the tangent is equal to the sine of the angle divided by the cosine.

For example, using the following right triangle, we can define the tangent of angle A as the length of side a (side opposite to A) divided by the length of side b (side adjacent to A).

Also, we can define the tangent of angle B as the length of side b (opposite side to B) divided by the length of side a (adjacent side).

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

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

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

Using the angles 90° and 270° in the calculator, we can see that we get a result of “Undefined”. This is due to the definition of the tangent.

Recall that the tangent can be defined as the sine of the angle over the cosine of the angle. Therefore, when we have a denominator equal to 0, we will get an “Undefined” result.

The cosine is equal to 0 when we have an angle of 90°. Also, this value repeats when we add or subtract 180°n, where n is any whole number. That is, the tangent of 90°+180°=270° is also undefined, and so on.

Graph of the tangent of an angle

We can extend the definition of the tangent to use values outside of a right triangle. In doing this, we can use both positive and negative angles.

The tangent function is periodic, that is, this function repeats itself after a constant interval. The period of the tangent function is equal to 180° or π.

Graph of tangent (radians and degrees)

Domain of the tangent of an angle

Using the graph of the tangent, we can see that we can use any input value, except for some specific points where the function approaches infinity.

The values that we cannot use are the asymptotes of the function and are equal to 90°+180°n, where n is either a positive or a negative integer.

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

Range of the tangent of an angle

Using the graph of the tangent, we can see that the output values do not have any restrictions. That is, the tangent function can result in any number, both positive and negative.

Therefore, the range of the tangent function is equal to all real numbers.

Table of the tangent of common angles

DegreesRadiansTangent
-90°-π/2Undefined
-60°-π/3-1.732051
-45°-π/4-1
-30°-π/6-0.577350
00
30°π/60.577350
45°π/41
60°π/31.732051
90°π/2Undefined

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