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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

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An arc of a circle:

circle graphic

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

red line

The formula for the arc length of a circle:

circle graphic

Arc length of a circle in radians:

Arc Length = circle graphic

Arc length of a circle in degrees:

Arc Length = circle graphic

red line

A sector of a circle:

circle graphic

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:

circle graphic

Sector area of a circle in radians:

Sector Area = circle graphic

Sector area of a circle in degrees:

Sector Area = circle graphic

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

circle graphic

circle graphic

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