L25 - Lecture 25 Section 4.1 Angles and Their Measure An...

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Lecture 25: Section 4.1 Angles and Their Measure An angle is formed by rotating a ray around its end- point. The starting position of the ray is the initial side oftheangle,andthepositionafterrotationisthe terminal side of the angle. The endpoint of the ray is called the vertex . An angle u1D703 is said to be in standard position if its vertexisintheoriginanditsinitialsidecoincideswith the positive u1D465 -axis. x y

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If therotation isin thecounterclockwisedirection, the angleis positive ;iftherotationisclockwise,theangle is negative . Angles u1D6FC and u1D6FD are coterminal angles if they have the same initial and terminal sides. x y x y A central angle is an angle whose vertex is at the center of a circle.
Radian Measure Def. One radian is a measure of the central angle that intercepts an arc whose length is equal to the radius. Algebraically, this means that u1D703 = u1D460 u1D45F where u1D703 is measured in radians. NOTE: For the angle u1D703 = 1 revolution: The length of the arc (circumference) u1D460 =2 u1D70Bu1D45F Therefore,

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