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Understanding the Unit Circle
What is the Unit Circle?
The unit circle is a circle with radius 1 centered at the origin (0,0). It's a fundamental tool in trigonometry that helps visualize and calculate trigonometric functions for any angle.
- Radius is always 1 unit
- Center is at (0,0)
- Any point (x,y) on the circle corresponds to (cos θ, sin θ)
- Angles are measured counterclockwise from the positive x-axis
Important Relationships
Coordinates:
x = cos θ
y = sin θ
Pythagorean Identity:
sin²θ + cos²θ = 1
Tangent Relationship:
tan θ = sin θ / cos θ
Applications
Mathematics
- Trigonometric functions
- Periodic motion
- Complex numbers
Physics
- Wave motion
- Circular motion
- Angular velocity