Tangent Calculator with Degrees

The tangent of an angle in a right-angled triangle is the ratio of the length of the opposite side to the length of the adjacent side. This calculator computes the tangent of any angle in degrees, providing both the numerical result and a visual representation of the trigonometric function.

What is Tangent?

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

tan(θ) = opposite / adjacent

The tangent function is periodic with a period of 180 degrees, meaning tan(θ) = tan(θ + 180°). The function is undefined when the angle is 90 degrees (π/2 radians) because the cosine of 90 degrees is zero, making the ratio undefined.

Note: The tangent function is undefined at 90° (π/2 radians) because the cosine of this angle is zero, leading to division by zero in the definition of tangent.

How to Use This Calculator

Using the tangent calculator with degrees is straightforward:

Enter the angle in degrees in the input field.
Click the "Calculate" button to compute the tangent of the angle.
The result will be displayed in the result panel, showing both the numerical value and a brief explanation.
Optionally, view the tangent curve visualization to understand the function's behavior.

The calculator handles all angles between -360° and 360°, providing accurate results for both positive and negative angles.

Formula

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

tan(θ) = sin(θ) / cos(θ)

Where:

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

This formula is derived from the definition of tangent in a right-angled triangle, where tan(θ) = opposite/adjacent, and the Pythagorean identity sin²(θ) + cos²(θ) = 1.

Examples

Here are some examples of tangent calculations for common angles:

Example 1: 30°

tan(30°) = sin(30°) / cos(30°) = (0.5) / (√3/2) ≈ 0.577

Example 2: 45°

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

Example 3: 60°

tan(60°) = sin(60°) / cos(60°) = (√3/2) / (0.5) ≈ 1.732

These examples demonstrate how the tangent function varies with different angles. The tangent calculator can compute the tangent for any angle within its domain.

FAQ

What is the difference between tangent and cotangent?

The tangent of an angle is the ratio of the sine to the cosine (tan(θ) = sin(θ)/cos(θ)), while the cotangent is the reciprocal of the tangent (cot(θ) = 1/tan(θ) = cos(θ)/sin(θ)). The cotangent is undefined at 0° and 180° where the sine is zero.

Why is the tangent function undefined at 90°?

The tangent function is undefined at 90° because the cosine of 90° is zero, leading to division by zero in the definition of tangent. This is a point where the tangent curve has a vertical asymptote.

How does the tangent function behave for angles greater than 90°?

The tangent function is periodic with a period of 180°, meaning tan(θ) = tan(θ + 180°). For angles between 90° and 270°, the tangent function is negative because the sine and cosine have opposite signs.