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The 22 pages that link to Unit circle, each with the reason it gives.

• CircleBroader topic: Its points encode trigonometric values by their coordinates.

• RadianBroader topic: On this circle, the numerical radian measure equals the length of the intercepted arc.

• AngleRelated: It represents angles as rotations and associates them with points on a circle.

• SineBroader topic: A point on this circle has sine as its vertical coordinate.

• Euler's formulaRelated: The real and imaginary parts give a point on this circle at angle θ.

• Trigonometric functionsRelated: Coordinates on this circle define sine and cosine for angles beyond triangle ranges.

• TrigonometryRelated: Its coordinates give sine and cosine for angles beyond acute triangle angles.

• PiRelated: Its circumference is 2π, making it central to trigonometric definitions.

• Root of unityRelated: Every complex root of unity lies on this circle.

• CosineRelated: Cosine is the horizontal coordinate of the point on this circle.

• Small-angle approximationRelated: Its arc length equals the angle in radians, giving geometric intuition for small-angle rules.

• Inverse trigonometric functionsNarrower topic: Its coordinates and angle conventions define the ratios these functions invert.

• TangentNarrower topic: Its coordinates make tangent the ratio of vertical to horizontal position.

• Euler's identityRelated: The value e^{iπ} is the point reached after a half-turn around this circle.

• Trigonometric identityNarrower topic: It gives geometric meaning to sine and cosine beyond acute triangle angles.

• Unit sphereCompared with: It is the two-dimensional analogue of the unit sphere.

• De Moivre's formulaRelated: Its angle-based coordinates give the geometric meaning of \(\cos\theta+i\sin\theta\).

• Sine and cosineRelated: A point at angle θ has coordinates (cos θ, sin θ) on this circle.

• Pythagorean trigonometric identityRelated: A point on it has coordinates cos θ and sin θ, whose squared lengths sum to one.

• Hadamard gap theoremBroader topic: For power series with radius one, this is the circle the theorem makes a natural boundary.

• F. and M. Riesz theoremNarrower topic: It is the domain on which the measure and its Fourier coefficients are defined.

• Niven's theoremRelated: It identifies sine with a coordinate and makes the theorem’s five possible values geometrically visible.