TrigonometryRADIANSRADIANSThis chapter will cover the measure of angles in terms of radians and degrees.EO 1.4 STATE the definition of a radian.RadianMeasureThe size of an angle is usually measured in degrees. However, in some applications the size ofan angle is measured in radians. A radian is defined in terms of the length of an arc subtendedby an angle at the center of a circle. An angle whose size is one radian subtends an arc whoselength equals the radius of the circle. Figure 4 shows BAC whose size is one radian. Thelength of arc BC equals the radius r of the circle. The size of an angle, in radians, equals thelength of the arc it subtends divided by the radius.(4-8)Figure 4 Radian AngleRadiansLength of ArcRadiusOne radian equals approximately 57.3 degrees. There areexactly 2p radians in a complete revolution. Thus 2pradians equals 360 degrees: p radians equals 180 degrees.Although the radian is defined in terms of the length of anarc, it can be used to measure any angle. Radian measureand degree measure can be converted directly. The size ofan angle in degrees is changed to radians by multiplyingby . The size of an angle in radians is changed top180degrees by multiplying by .180pExample:Change 68.6° to radians.068.6°p180(68.6)p1801.20 radiansRev. 0 Page 9 MA-04
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