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Degrees Unit Circle Calculator

Reviewed by Calculator Editorial Team

The Degrees Unit Circle Calculator helps you determine trigonometric values (sine, cosine, tangent) for any angle in degrees. This tool is essential for students, engineers, and anyone working with trigonometry, physics, or geometry.

What is a Unit Circle?

A unit circle is a circle with a radius of 1 centered at the origin (0,0) in the coordinate plane. It's a fundamental concept in trigonometry that helps visualize and calculate trigonometric functions.

The unit circle is 360 degrees, with 0 degrees pointing to the right (along the positive x-axis). As you move counterclockwise, the angle increases. The coordinates of any point on the unit circle correspond to the cosine and sine of that angle.

Key points on the unit circle:

  • 0°: (1, 0)
  • 90°: (0, 1)
  • 180°: (-1, 0)
  • 270°: (0, -1)
  • 360°: (1, 0)

How to Use This Calculator

  1. Enter the angle in degrees in the input field
  2. Click the "Calculate" button
  3. View the results for sine, cosine, and tangent
  4. Use the chart to visualize the angle on the unit circle

The calculator will display the trigonometric values rounded to 4 decimal places. You can also see a visual representation of the angle on the unit circle.

Formula Used

The trigonometric functions for a unit circle are calculated using the following formulas:

  • sin(θ) = y-coordinate of the point on the unit circle at angle θ
  • cos(θ) = x-coordinate of the point on the unit circle at angle θ
  • tan(θ) = sin(θ)/cos(θ) = y/x

Where θ is the angle in degrees, and the point (x,y) lies on the unit circle.

Worked Example

Let's calculate the trigonometric values for 45 degrees:

  1. Convert 45 degrees to radians: 45 × (π/180) ≈ 0.7854 radians
  2. Calculate sin(45°): sin(0.7854) ≈ 0.7071
  3. Calculate cos(45°): cos(0.7854) ≈ 0.7071
  4. Calculate tan(45°): 0.7071 / 0.7071 ≈ 1.0000

These values correspond to the coordinates (0.7071, 0.7071) on the unit circle at 45 degrees.

FAQ

What is the difference between degrees and radians?
A full circle is 360 degrees or 2π radians. Degrees are commonly used in everyday applications, while radians are more common in advanced mathematics and physics.
How do I convert degrees to radians?
Multiply the angle in degrees by π/180 to convert to radians.
What are the trigonometric values for 0 degrees?
For 0 degrees, sin(0°) = 0, cos(0°) = 1, and tan(0°) = 0.
Can I use negative angles with this calculator?
Yes, the calculator accepts negative angles. Negative angles are measured clockwise from the positive x-axis.
What are the trigonometric values for 360 degrees?
For 360 degrees, sin(360°) = 0, cos(360°) = 1, and tan(360°) = 0, which is the same as 0 degrees.