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 h AB = 1 4 C = π 2 r 90 (a) θ = 90 O A B h AB = 1 2 C = π r 180 (b) θ = 180 O A B h AB = C = 2 π r 360 (c) θ = 360 Figure 4.1.1 Angle θ and intercepted arc h 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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Unformatted text preview: ◦ cuts off an arc of length 2 π r , which is the same as the circumference of the circle. So associating the central angle with its intercepted arc, we could say, for example, that 360 ◦ “equals” 2 π r (or 2 π ‘radiuses’). The radius r was arbitrary, but the 2 π in front of it stays the same. So instead of using the awkward “radiuses” or “radii”, we use the term radians : 360 ◦ = 2 π radians (4.1) The above relation gives us any easy way to convert between degrees and radians: Degrees to radians: x degrees = p π 180 · x P radians (4.2) Radians to degrees: x radians = ± 180 π · x ² degrees (4.3) 87...
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.

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