Arcotangent

Online arctangent calculatori.e., the inverse operation to the tangent that will allow you to know the angle in degrees or radians associated to a value of this trigonometric ratio.

The operation of this arctangent calculator is very simple. All you have to do is enter the arctan valueClick on the calculate button and select whether you want the result in degrees (°) or in radians (rad).

What is the arctangent?

As we have said before, the arctangent is the inverse of the tangent function:

arctan(y) = tan-1(y) = x+

That is the mathematical formula or the correct way to write that we are going to calculate the arctan of a particular value. Let's see it with some examples below.

Arcotangent of 1

For example, we know that the tangent of 45º is equal to 1, therefore, at apply the arctangent of 1 we obtain the starting angle which is 45 degrees:

arctan(1) = tan-1(1) = 45°

Arcotangent of 0

Now we are going to do the same as in the previous example but this time with the value zero, one of the most common questions when we talk about the arctan function. We are going to calculate the arctangent in this case and, subsequently, analyze the result obtained:

arctan(0) = tan-1(0) = 0°

Is this an expected result? Yes, since the tangent of zero also has that value, i.e. 0. To make it clearer what we are saying, below you have a graph in which you can see how the function passes through the origin and what we have just said is verified.

Arcotangent of infinity

¿What is the arctangent of infinity? or minus infinity? In this case, we have to make use of limits to solve this problem.

If we want to calculate the arctangent of infinitywe see that the limit is equal to π/2 or 90º:

Arcotangent of infinity

If what we want to know is the arctangent of minus infinitythen we have the same result but with a minus sign.

Arcotangent of minus infinity

Graph of the arctangent function

Arctangent graph

In this chart above you can see the appearance of the arctangent function for a bounded interval of values having towards π/2 and towards - π/2

Table of the arctangent function

Online arctangent calculator

Below you have a arctangent table which includes the most commonly used values in trigonometric problems or those involving this trigonometric function:

yx = arctan(y) in degreesx = arctan(y) in radians
-1,732050808-60°-π/3
-1-45°-π/4
-0,577350269-30°-π/6
00
0,57735026930°π/6
145°π/4
1,73205080860°π/3

Characteristics of the arctangent

We finish the section dedicated to this trigonometric function by talking a little bit about the properties of the arctangent, including its domain, path, derivative and integral.

Domain

The function arctan(y) has a domain that ranges from from minus infinity to plus infinityThere is no cut in this interval. Therefore, we can say that all real numbers are included:

arctan(y) :[-∞ , +∞]

This can be seen in the graph above.

Tour

In this case, and we can check it in the graph, the path goes from [- π/2 , π/2] to [- π/2 , π/2].

Due to the two previous properties, we can say that the arctangent function is continuous and increasing in all R.

Arctangent derivative

This is the formula that we obtain when calculating the derivative of the arctan x:

Derivative of the arctangent

If instead of x we have a function u, then it can be said that the derivative of arctangent of a function is equal to the derivative of that function divided by one plus the function squared. This is expressed as follows:

Formula of the arctangent derivative

Integral

Finally, this is the integral obtained for the function:

Integral of the arctangent

Calculate the arctangent in Excel

Excel incorporates a function that allows you to calculate the arctangent directly and without calculations. Simply open a new spreadsheet and type the following formula in an empty cell:

=ATAN()

You must take into account that between the brackets you must write the value of the number for which you want to obtain its arctangent, in addition, the result that Excel gives by default will be expressed in radians in the range covering [- π/2 , π/2].

As a practical example, we will calculate the arctangent of 2 in Exscel,

=ATAN(2)

That will give us a result of 1.107148718 radians but if we want to express it in degreeswe will have to write the formula as follows:

=DEGREES(ATAN(2))

This will give us a result of 63.43494882 degrees for the arctangent of 2. Depending on the unit you need, you will have to use one or another Excel formula to get the arctangent of 2. arctangent of a number.

Arcotangent in the iPhone calculator

Arcotangent in the iPhone calculator

The iPhone calculator allows you to do the ATAN (inverse of the tangent) but it has an unintuitive method, so you may not know how to do it.

To do this, the first thing you must do is disable the screen rotation lock if you had it enabled. Then go into the calculator application, rotate the mobile 90º to put it in landscape mode and you will have access to the scientific version of the app.

Now, press that button that says 2ndIf you want to know its arctangent, type the number for which you want to know its arctangent and when you have done so, press the key on which is written "tan-1".

How to use the online arctangent calculator

Calculate the arctangent online is something that many of you want so that you don't have to use the calculator, so we have recorded a video in which we explain how to use our calculator so that you don't have any doubts about the process to follow.

The only thing you should bear in mind is that in the face of calculate the arctag of a number decimal, you must use as separator a . instead of the comma (,) otherwise, it will only take the integer part and the resulting angle will not be the one you are really looking for.

5 thoughts on “Arcotangente”

    • Hi Lola,

      Thank you very much for your comment. If you need any help to solve the arctangent or any other trigonometric ratio do not hesitate to ask us, ok?

      Best regards!

    • Hello Jhafer,

      The arctangent of 0.5 is = tan-¹ 0.5 = 26º 33′ 54.184″ = 26.56505118º+k×180º (k=..-1,0,1,..) = -153.43494882º, 26.56505118º, 206.56505118º, .. = 0.46364761rad+k×π (k=..-1,0,0,1,..) = -0.85241638π, 0.14758362π, 1.14758362π,

      Best regards!

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