Stitz-Zeager_College_Algebra_e-book

Sin it is high time for an example example 1031 find

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online