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The unit circle is a circle with radius 1 centred at the origin. It provides the foundation for trigonometry — the sine and cosine of any angle equal the y and x coordinates of the corresponding point on the circle.
공식
x² + y² = 1; point = (cos θ, sin θ)
- θ
- angle from positive x-axis (radians or degrees)
- x
- x-coordinate (cosine value) (dimensionless)
- y
- y-coordinate (sine value) (dimensionless)
단계별 가이드
- 1For angle θ: point = (cos θ, sin θ)
- 2sin²θ + cos²θ = 1 (Pythagorean identity)
- 3tan θ = sin θ / cos θ
- 4Angles repeat every 360° (2π radians)
풀어진 예시
입력
θ = 30°
결과
sin = 0.5, cos = √3/2 ≈ 0.866, tan ≈ 0.577
입력
θ = 45°
결과
sin = cos = 1/√2 ≈ 0.707, tan = 1
자주 묻는 질문
Why is the unit circle important?
The unit circle extends trigonometry beyond triangles. Every angle and its trig values map directly to circle coordinates.
What does the Pythagorean identity sin²θ + cos²θ = 1 represent on the unit circle?
It states that any point (cos θ, sin θ) on the unit circle satisfies the circle equation x² + y² = 1.
How many degrees are in one full rotation on the unit circle?
360° or 2π radians. After that, angles repeat with the same sine and cosine values.
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