Stitz-Zeager_College_Algebra_e-book

Sin it is high time for an example example 1031 find

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Unformatted text preview: ar from obvious and leads to a counterintuitive scenario which is explored in the Exercises. Since the diameter of a circle is twice its radius, we can quickly rearrange the equation in Definition 10.1 to get a formula more useful for our purposes, namely: π= 10.1 Angles and their Measure 601 2π = C r This tells us that for any circle, the ratio of its circumference to its radius is also always constant; in this case the constant is 2π . Suppose now we take a portion of the circle, so instead of comparing the entire circumference C to the radius, we compare some arc measuring s units in length to the radius, as depicted below. Let θ be the central angle subtended by this arc, that is, an angle whose vertex is the center of the circle and whose determining rays pass through the endpoints s of the arc. Using proportionality arguments, it stands to reason that the ratio r should also be a constant among all circles, and it is this ratio which defines the radian measure of an angle. s r θ r The radian...
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