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Tan Calculator Degrees

Reviewed by Calculator Editorial Team

This tan calculator degrees tool helps you compute the tangent of an angle in degrees. Simply enter your angle in degrees and get the precise tangent value. The calculator also provides a visual representation of the tangent function.

How to Use This Calculator

Using the tan calculator degrees is straightforward:

  1. Enter the angle in degrees in the input field.
  2. Click the "Calculate" button to compute the tangent value.
  3. View the result in the result panel below.
  4. Use the chart to visualize the tangent function for the entered angle.

The calculator will display the tangent value and show it on the chart. You can also reset the calculator to start over.

Formula Explained

The tangent of an angle 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 the angle
  • cos(θ) is the cosine of the angle

The calculator converts the angle from degrees to radians before performing the calculation since JavaScript's Math.tan() function uses radians.

Worked Examples

Example 1: Calculating tan(30°)

To calculate tan(30°):

  1. Convert 30° to radians: 30° × (π/180) ≈ 0.5236 radians
  2. Compute tan(0.5236) ≈ 0.5774

The result is approximately 0.5774.

Example 2: Calculating tan(45°)

To calculate tan(45°):

  1. Convert 45° to radians: 45° × (π/180) ≈ 0.7854 radians
  2. Compute tan(0.7854) ≈ 1.0000

The result is exactly 1.0000.

Example 3: Calculating tan(60°)

To calculate tan(60°):

  1. Convert 60° to radians: 60° × (π/180) ≈ 1.0472 radians
  2. Compute tan(1.0472) ≈ 1.7321

The result is approximately 1.7321.

Frequently Asked Questions

What is the tangent function?
The tangent function is a trigonometric function that relates the angle of a right triangle to the ratio of the opposite side to the adjacent side. It's periodic with a period of π radians (180°).
How do I convert degrees to radians?
To convert degrees to radians, multiply the degree value by π/180. For example, 30° × (π/180) ≈ 0.5236 radians.
What is the range of the tangent function?
The tangent function has a range of all real numbers (-∞, ∞). It's undefined where the cosine function is zero (i.e., at 90° + k×180° for any integer k).
Can I use this calculator for angles outside 0° to 360°?
Yes, the calculator can handle any angle value, but the tangent function is periodic with a period of 180°, so tan(θ) = tan(θ + k×180°) for any integer k.
Is the tangent function odd or even?
The tangent function is odd, meaning tan(-θ) = -tan(θ) for any angle θ.