45°
The Unit Circle
The unit circle is a circle with radius 1 centered at the origin. Any point on the circle has coordinates (cos θ, sin θ) where θ is the angle from the positive x-axis.
cos²θ + sin²θ = 1
Trig Functions
- cos θ = x-coordinate = adjacent / hypotenuse
- sin θ = y-coordinate = opposite / hypotenuse
- tan θ = sin θ / cos θ = slope of the radius
tan θ = sin θ⁄cos θ
Sign by Quadrant
- QI (0°-90°): sin +, cos +, tan +
- QII (90°-180°): sin +, cos −, tan −
- QIII (180°-270°): sin −, cos −, tan +
- QIV (270°-360°): sin −, cos +, tan −
How to Use
• Drag the slider to change the angle θ
• Click Animate to auto-rotate around the circle
• Watch sin, cos, and tan update in real-time
• The red vertical line = sin θ (y-coordinate)
• The blue horizontal line = cos θ (x-coordinate)
• The yellow dashed line = tan θ
Did You Know?
The word "sine" comes from the Latin sinus meaning "bay" or "fold", mistranslated from the Arabic jiba. The tangent function gets its name from the line that just "touches" (tangit in Latin) the circle at one point.