Arcs, Sectors & Segments

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Presentation transcript:

Arcs, Sectors & Segments

Radian Measure Degrees Radians Radians Degrees The degree system is based on dividing a circle into 360 equal sectors, the measure of each being “one degree” The radian system is based on the relationship between the radius and the arc length of a sector. Therefore: measure of an angle in radians = ___________________ Angle measure (in radians) in a circle: Converting from Degrees to Radians and from Radians to Degrees Degrees Radians Radians Degrees Angle in Degrees Π . 180 Angle in Radians Angle in Radians 180 Π Angle in Degrees

Arc Length Recall: RADIAN MEASURE ARC LENGTH Radian Definition: One radian is defined as the size of an angle needed to cut off an arc of the same length as the radius ARC LENGTH Arc: part of the circumference of a circle.

Area of a Sector Sector: Perimeter of a Sector: Area of a Sector: a 2D shape bound by 2 radii and the included arc of a circle the area of a sector is a fraction of the area of a whole circle Perimeter of a Sector: Area of a Sector:

Examples

Example

Examples

Example