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Pre-Calc Exam Notes 87

# Pre-Calc Exam Notes 87 - ◦ cuts off an arc of length 2 π...

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4 Radian Measure 4.1 Radians and Degrees So far we have been using degrees as our unit of measurement for angles. However, there is another way of measuring angles that is often more convenient. The idea is simple: associate a central angle of a circle with the arc that it intercepts. Consider a circle of radius r > 0, as in Figure 4.1.1. In geometry you learned that the circumference C of the circle is C = 2 π r , where π = 3 . 14159265 ... . O A B hbracewidest AB = 1 4 C = π 2 r 90 (a) θ = 90 O A B hbracewidest AB = 1 2 C = π r 180 (b) θ = 180 O A B hbracewidest AB = C = 2 π r 360 (c) θ = 360 Figure 4.1.1 Angle θ and intercepted arc hbracewidest AB on circle of circumference C = 2 π r In Figure 4.1.1 we see that a central angle of 90 cuts off an arc of length π 2 r , a central angle of 180 cuts off an arc of length π r , and a central angle of 360
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