Degrees Tangent Calculator

The degrees tangent calculator computes the tangent of an angle given in degrees. Tangent is one of the primary trigonometric functions, essential in geometry, physics, and engineering. This guide explains how to use the calculator, understand the results, and interpret tangent values.

What is Tangent?

Tangent (tan) is a trigonometric function that relates the angle of a right triangle to the ratio of the opposite side to the adjacent side. In the unit circle, tangent represents the y-coordinate divided by the x-coordinate of a point corresponding to a given angle.

Key properties of tangent:

tan(θ) = opposite/adjacent
tan(θ) = sin(θ)/cos(θ)
Periodic with period π (180°)
Undefined at θ = 90° + k*180° (where k is an integer)

Tangent is undefined at 90° and 270° because the cosine of these angles is zero, making the division undefined.

Degrees Tangent Formula

The tangent of an angle θ in degrees is calculated using the following formula:

tan(θ) = sin(θ) / cos(θ)

Where:

θ is the angle in degrees
sin(θ) is the sine of θ
cos(θ) is the cosine of θ

Most calculators and programming languages use radians for trigonometric functions. To calculate tangent in degrees, you must first convert degrees to radians:

tan(θ°) = tan(θ° × π/180)

How to Use the Calculator

Enter the angle in degrees in the input field
Click "Calculate" to compute the tangent
View the result in the result panel
Use the chart to visualize the tangent function
Click "Reset" to clear the inputs

For angles where tangent is undefined (90°, 270°, etc.), the calculator will display "Undefined".

Examples

Example 1: Calculating tan(45°)

Using the formula:

tan(45°) = sin(45°)/cos(45°) = (√2/2)/(√2/2) = 1

The calculator confirms that tan(45°) = 1.

Example 2: Calculating tan(30°)

Using the formula:

tan(30°) = sin(30°)/cos(30°) = (1/2)/(√3/2) = 1/√3 ≈ 0.577

The calculator shows tan(30°) ≈ 0.577.

Example 3: Calculating tan(90°)

tan(90°) is undefined because cos(90°) = 0.

The calculator will display "Undefined" for this input.

FAQ

What is the difference between tangent and cotangent?

Tangent (tan) is the ratio of the opposite side to the adjacent side in a right triangle. Cotangent (cot) is the reciprocal of tangent: cot(θ) = 1/tan(θ).

Why is tangent undefined at 90°?

At 90°, the cosine of the angle is zero, making the division sin(θ)/cos(θ) undefined. This occurs because the adjacent side of the right triangle becomes zero.

How do I convert tangent to degrees?

To convert a tangent value to degrees, use the arctangent function (atan) and then multiply by 180/π to convert from radians to degrees.