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Degrees Calculator Sin Cos Tan

Reviewed by Calculator Editorial Team

This degrees calculator computes the sine, cosine, and tangent of angles in degrees. It provides precise trigonometric values and visualizes the results on a unit circle. The calculator follows standard trigonometric formulas and handles all angle ranges.

How to Use This Calculator

To calculate trigonometric values for an angle in degrees:

  1. Enter the angle in degrees in the input field
  2. Click the "Calculate" button
  3. View the sine, cosine, and tangent values
  4. Examine the unit circle visualization

The calculator accepts angles from -360° to 360° and provides results with up to 6 decimal places of precision.

Trigonometric Formulas

The calculator uses these standard trigonometric formulas for degree-based calculations:

sin(θ) = opposite/hypotenuse
cos(θ) = adjacent/hypotenuse
tan(θ) = opposite/adjacent = sin(θ)/cos(θ)

Where θ is the angle in degrees, and the values are derived from the unit circle where the hypotenuse is always 1.

Worked Examples

Example 1: 30° Angle

For θ = 30°:

  • sin(30°) = 0.5
  • cos(30°) = √3/2 ≈ 0.866
  • tan(30°) = √3/3 ≈ 0.577

Example 2: 45° Angle

For θ = 45°:

  • sin(45°) = √2/2 ≈ 0.707
  • cos(45°) = √2/2 ≈ 0.707
  • tan(45°) = 1

Interpreting Results

The sine, cosine, and tangent values represent:

  • Sine: The y-coordinate on the unit circle
  • Cosine: The x-coordinate on the unit circle
  • Tangent: The slope of the line from the origin to the point on the unit circle

Note: The tangent function is undefined when cosine is zero (at 90° and 270° angles).

Frequently Asked Questions

What is the difference between degrees and radians?

A full circle is 360° or 2π radians. Degrees are commonly used in everyday applications, while radians are more common in advanced mathematics and physics.

Why does the tangent function have undefined values?

The tangent function is undefined when the cosine of the angle is zero, which occurs at 90° and 270° angles. This is because division by zero is undefined in mathematics.

How accurate are the calculator results?

The calculator provides results with up to 6 decimal places of precision, which is sufficient for most practical applications. For higher precision needs, specialized scientific calculators may be required.