Unit Circle Calculator (Angles, Coordinates, Trig Values)
🧮 Unit Circle Calculator
Enter Angle:
or
Or Enter Coordinates:
⭕ Interactive Unit Circle
⭕ Unit Circle Calculator
Interactive calculator for working with the unit circle. Find point coordinates, calculate trigonometric functions, and visualize results. Perfect assistant for mastering trigonometry.
🔍 Calculator Features:
- Calculator - find coordinates and trigonometric values
- Visualization - interactive unit circle
- Exact Values - display exact trigonometric values for standard angles
📝 What is the Unit Circle:
The unit circle is a circle with radius 1 centered at the origin. On it:
- x-coordinate of point = cos(θ)
- y-coordinate of point = sin(θ)
- Full rotation = 360° = 2π radians
- First quadrant: 0° - 90°
- Second quadrant: 90° - 180°
- Third quadrant: 180° - 270°
- Fourth quadrant: 270° - 360°
Frequently Asked Questions
What is the unit circle?
The unit circle is a circle with radius 1 centered at the origin (0,0). It's used to define trigonometric functions.
How are point coordinates on the unit circle related to trigonometric functions?
For angle θ: the x-coordinate of the point on the unit circle equals cos(θ), and the y-coordinate equals sin(θ).
Why is it important to know the unit circle?
The unit circle helps visualize trigonometric functions, their periodicity, and relationships between different angles.
What are the key points to remember on the unit circle?
Key points: 0°, 30°, 45°, 60°, 90°, 120°, 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, 330°, 360°.
How do you remember trigonometric values?
Practice with the unit circle, use patterns (like 30-60-90 and 45-45-90 triangles), and remember that coordinates give you cos and sin values directly.
What are the coordinates for angle 0°?
For angle 0°: coordinates (1, 0), cos(0°) = 1, sin(0°) = 0.
What are the coordinates for angle 90°?
For angle 90°: coordinates (0, 1), cos(90°) = 0, sin(90°) = 1.
How to find angle from known coordinates?
Use the arctan2(y, x) function or enter coordinates in the calculator and click 'Find Angle'.
What is sin(30°)?
sin(30°) = 1/2 = 0.5
What is cos(45°)?
cos(45°) = √2/2 ≈ 0.7071
What signs do trigonometric functions have in different quadrants?
Quadrant I: sin > 0, cos > 0; Quadrant II: sin > 0, cos < 0; Quadrant III: sin < 0, cos < 0; Quadrant IV: sin < 0, cos > 0.