Tangent

Calculates the tangent of any angle with our tool. Enter the angle in degrees or radians and press the calculate button to obtain its tangent.

We also have available calculators for sine and cosine calculations so if they are of help to you, here are the links that will take you to each one of them.

How to calculate the tangent

Triangle to calculate trigonometric ratios

To calculate the tangent in a right triangle, we simply have to do the division of the opposite side divided by the adjoining side, that is:

tan θ = opposite cathetus / adjacent cathetus

By example.Let's imagine that we have a right triangle whose opposite leg measures 3 centimeters and the adjoining leg has a length of 7 cm. With these data, the sine would be calculated as follows:

tan θ = 3 cm / 7 cm = 0.428

If we know the value of sine and cosine, another way of calculating the value of the tangent is to apply the following mathematical formula:

tan θ = sin θ / cos θ

Both ways of calculating the tangent value are valid. but we will use one or the other depending on the starting data we have.

Graphical representation of the tangent function

Tangent function

In the graph above you can see the shape of this trigonometric function.

Tangent function table

Online tangent calculator

Working with the tangent function is more convenient if we have a table that collects the tangent of the most common angles in the math problems. Note that the tangent is the sine divided by the cosine, so for angles of 90 degrees and 270 degrees we find that the trigonometric function is not defined and tends to infinity.

GradesRadiansTangent
00
30ºπ/60.577
45ºπ/41
60ºπ/31.732
90ºπ/2Infinity
180ºπ0
270º3π/2Infinity
360º0

Tangent of 30 equals 0.577. This is one of the most frequent doubts that you have and that you ask us the most on a daily basis.

Derivative of the tangent

If you want to calculate the derivative of the tangent of xIf you do not know the derivative of the tangent of x, it is best to write the equivalence of the tangent in terms of the sine and cosine of x since we do know these derivatives. We solve and we would be left with the derivative of the tangent of x is:

Derivative of the tangent of x

If instead of having the variable x we have a function, then the derivative of the tangent of a function gets a little more complicated:

Derivative of the tangent of a function

In this second case, the derivative of the TAN of a function will be equal to the derivative of that function times 1 plus the tangent to the square of that function.

Integral of the tangent

Below you can see which is the integral of the tangent of x:

∫ tan x dx = -ln|cos x| + C

How the tangent calculator works

Our online tangent calculator has a very simple operation. All you have to do is enter the angle in the corresponding box and select the unit, either in degrees or in radians if you prefer.

For example, if you want to calculate the tangent of 30 degrees, you will only have to type the number and leave the units as they are since by default our tangent calculator works with degrees.

That is the basic operation, we told you at the beginning that it is very easy to use.

How to calculate the tangent in Excel

If you want to create your own calculator to find the tangentyou can make one using Excel. The Microsoft program has a dedicated function to solve this trigonometry function that works as follows.

Open a new spreadsheet and in an empty cell type the following function to get the tangent of an angle:

=TAN()

In parentheses you have to write the angle in radians since by default that is the input argument.

If you want to make the calculation of the tangent in Excel with an angle in degreesthen you must write the function in this form:

=TAN(RADIANS(90))

In the example above we have calculated the tangent of 90 degrees but you can substitute that number for the angle in degrees that you want.

If you have any doubt about this trigonometry function, write us a comment and we will help you. And if you liked our work you can also leave us a comment :)

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