. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . THE CIRCULAR MEASURE. 7 .\ angle AOB : 4rt. angles :: arc AB : circumference, :: r : 2vr :: 1 : 2w. -, A ,-vd 4 rt. angles 2 rt. angle AOB = —^— = § .-. a radian = angle AOB = *f?° = 57°.2957795 = = Therefore, the radian is the same for all circles, and= 57°.2957795. Let ABP be any circle; let the angleAOB be the radian; and let AOP beany other angle. Then arc AB = radius OA. .-. angle AOP : angle AOB :: arc AP : arc AB ;or angle AOP : radia
. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . THE CIRCULAR MEASURE. 7 .\ angle AOB : 4rt. angles :: arc AB : circumference, :: r : 2vr :: 1 : 2w. -, A ,-vd 4 rt. angles 2 rt. angle AOB = —^— = § .-. a radian = angle AOB = *f?° = 57°.2957795 = = Therefore, the radian is the same for all circles, and= 57°.2957795. Let ABP be any circle; let the angleAOB be the radian; and let AOP beany other angle. Then arc AB = radius OA. .-. angle AOP : angle AOB :: arc AP : arc AB ;or angle AOP : radian : : arc AP : radius. .-. angle AOP = ;— x radian. radius The measure of any quantity is the number of times itcontains the unit of measure (Art. 2). ,\ the circular measure of angle AOP = : radius Note 1. — The student will notice that a radian is a little less than an angle of anequilateral triangle, , of 60°. Angles expressed in circular measure are usually denoted by Greek letters, a, j3,y, ..., , 9, i//, .... The circular measure is employed in the various branches of Analytical Mathe
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