1 resource radian measure and arc length
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This document discusses radian measure and its use in measuring angles and arcs in circles. It defines a radian as the angle subtended at the center of a circle by an arc equal in length to the radius. The document provides formulas for converting between radian and degree measures. Specifically, it states that 1 radian is equal to 180/ degrees, or approximately 57.3 degrees. Examples are given to demonstrate calculating radian measures given arc lengths and radii, and to convert between radians and degrees.
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1 resource radian measure and arc length
- 1. Radian measureArc lengthArea of sectorRadian measure use in trigonometryCircular Measure
- 2. Properties of A CircleWhat do we know about Circle?Minor SectorArcArea = r2Circumference = 2r/ d
- 3. Finding Arc Length & Area of Sector
- 4. Radian MeasureThe limitation of degree measurement requires another circular measure which is radian.The angle subtended at the centre of a circle by an arc are equal in length to the radius is 1 radian
- 5. Radian MeasureLength of arc APC = 2rLength of arc APD = 3rLength of arc APE = 3.6rAOC = 2 radiansAOD = 3 radiansAOE = 3.6 radiansSo, how do we determine the radian measure given the arc length and the radius of the circle?
- 6. Radian MeasureIn general, if the length of arc, s units and the radius is r units, then That is the size of the angle (慮) is given by the ratio of the arc length to the length of the radius.For example:If s = 3 cm and r = 2 cm, then
- 7. Relation between Radian and Degree MeasureConsider the angle 慮 in a semicircle of radius r as shown below. Then,We can concludeFurthermore,
- 8. Convertion between Degree & RadianDEGREERADIAN
- 9. Relation between Radian and Degree MeasureExample 1:Solution:
- 10. Relation between Radian and Degree MeasureExample 2:Solution:
- 11. Classwork
- 12. ReferencesThong, Ho Soo, Msc, Dip Ed; Hiong, Khor Nyak, Bsc, Dip Ed; New Additional Mathematics pg. 280 - 292, SNP Panpac Pte Ltd, Singapore 2005.