Tangent Calculator – Calculate tan(x)
Find the tangent of an angle using the tan calculator below. Start by entering the angle in degrees or radians.
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How to Find the Tangent of an Angle
In a right triangle, the tangent of angle α, or tan(α), is the ratio between the angle’s adjacent side and the opposite side.
Tangent is one of the three primary trigonometric functions and is abbreviated tan.
You might be asking how to find the tangent of an angle? Use the formula below to calculate tan.
The tangent formula is:
tan(α) = opposite a / adjacent b
Thus, the tangent of angle α in a right triangle is equal to the opposite side’s length divided by the adjacent side’s length.
To solve tan, simply enter the length of the opposite and adjacent and solve.
For example, let’s calculate the tangent of angle α in a triangle with the length of the opposite side equal to 4 and the adjacent equal to 8.
tan(α) = 4 / 8
tan(α) = 1 / 2
If you graph the tangent function for every possible angle, it forms multiple curves from lower values to higher that never touch the angles at 90° or 270° increments.
The table below shows common angles and the tan value for each of them.
|Angle (degrees)||Angle (radians)||Tangent|
|30°||π / 6||1 / √3 = √3 / 3|
|45°||π / 4||1|
|60°||π / 3||√3|
|90°||π / 2||undefined|
|120°||2π / 3||-√3|
|135°||3π / 4||-1|
|150°||5π / 6||–1 / √3 = –√3 / 3|
|210°||7π / 6||1 / √3 = √3 / 3|
|225°||5π / 4||1|
|240°||4π / 3||√3|
|270°||3π / 2||undefined|
|300°||5π / 3||-√3|
|315°||7π / 4||-1|
|330°||11π / 6||–1 / √3 = –√3 / 3|
Inverse Tangent and Cotangent
The inverse of the tangent function is the arctan function. Thus, if you know the tan of an angle, you can use arctan to find the angle.
Cotangent, on the other hand, is the reciprocal of the tangent value. The following formulas show the relationship between tangent and cotangent.
tan(α) = opposite / adjacent
cot(α) = adjacent / opposite = 1 / tan(α)