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The Trigonometry of Circles

Definitions and formulas for the arc and the arc length of a circle, sector and the area of the sector of a circle, the unit circle, the angles on the unit circle in radians, the angles on the unit circle in degrees, the points on the circumference of the unit circle
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arc of a circle arc length of a circle sector of a circle
area of a sector of a circle the unit circle points on the circumference
of the unit circle

 

An arc of a circle:

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An arc of a circle is a segment of the circumference of the circle.

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The formula for the arc length of a circle:

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Arc length of a circle in radians:

Arc Length circle graphic

Arc length of a circle in degrees:

Arc Length circle graphic

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A sector of a circle:

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A sector of a circle is a pie shaped portion of the area of the circle.  Technically, the piece of pie is between two segments coming out of the center of the circle.

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The area of a sector of a circle:

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Sector area of a circle in radians:

Sector Area circle graphic

Sector area of a circle in degrees:

Sector Area circle graphic

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The unit circle:
 The main angles of the unit circle in radians: The main angles of the unit circle in degrees:

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circle graphic

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