Tangent to Degrees Calculator

What is Tangent?

In trigonometry, the tangent of an angle (often written as tan) is one of the primary trigonometric functions. For a right-angled triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

Tangent is a periodic function with a period of 180 degrees, meaning tan(θ) = tan(θ + 180°n) for any integer n. The tangent function is undefined when the cosine of the angle is zero (i.e., when the angle is 90° + 180°n).

How to Calculate Tangent

To calculate the tangent of an angle in degrees, you can use the following steps:

1. Convert the angle from degrees to radians if necessary (though most calculators can handle degrees directly).
2. Use the tangent formula: tan(θ) = opposite/adjacent.
3. For angles outside the standard right-angled triangle, use the unit circle definition where tan(θ) = sin(θ)/cos(θ).

This calculator automates these steps for you.

Tangent Formula

The tangent function can also be expressed in terms of sine and cosine:

Tangent Examples

Let's look at a few examples of calculating the tangent of angles in degrees.

Example 1: 30° Angle

For a 30° angle in a right-angled triangle with opposite side 1 and adjacent side √3:

Example 2: 45° Angle

For a 45° angle in a right-angled triangle with equal opposite and adjacent sides (1 each):

Example 3: 60° Angle

For a 60° angle in a right-angled triangle with opposite side √3 and adjacent side 1:

Tangent Chart

The tangent function has a characteristic pattern that repeats every 180 degrees. Here's a chart showing the tangent values for angles from 0° to 360°: