Right Triangle Definitions

Trigonometry · Axiom Academy

LESSON Right Triangle Definitions Connecting the unit circle coordinate approach with traditional right triangle ratios On the unit circle (radius = 1), we define an angle θ by rotating counterclockwise from the positive x-axis. The point where this angle intersects the circle has coordinates (x, y). cos θ = x-coordinate of the point sin θ = y-coordinate of the point Now let's drop a perpendicular line from our point on the circle down to the x-axis. This creates a right triangle! The triangle has: Hypotenuse: the radius (which equals 1) Adjacent side: horizontal distance from origin (the x-coordinate) Opposite side: vertical distance (the y-coordinate) Here's where it all comes together! The traditional right triangle definitions are: 4. All Six Trigonometric Functions Both approaches extend naturally to all six trigonometric functions:

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