Defining Sine and Cosine

Trigonometry · Axiom Academy

LESSON Defining Sine and Cosine Understanding sine and cosine through the unit circle: how these fundamental trigonometric functions emerge from coordinates on a circle of radius 1. The unit circle is a circle with radius 1 centered at the origin (0, 0) in the coordinate plane. Every point on this circle is exactly 1 unit away from the center. For any angle θ measured counterclockwise from the positive x-axis, we can draw a ray from the origin at that angle. Where this ray intersects the unit circle, the x-coordinate of that point is defined as cos(θ) . Similarly, for the same angle θ, the y-coordinate of the point where the ray intersects the unit circle is defined as sin(θ) . As the angle θ increases from 0° to 360°, the point on the unit circle traces a complete revolution. Watch how the sine and cosine values change smoothly, creating the characteristic wave patterns.

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