Unformatted text preview: measure of θ is s
r Using this deﬁnition, one revolution has radian measure 2πr = 2π , and from this we can ﬁnd
the radian measure of other central angles using proportions, just like we did with degrees. For
instance, half of a revolution has radian measure 2 (2π ) = π , a quarter revolution has radian
measure 4 (2π ) = 2 , and so forth. Note that, by deﬁnition, the radian measure of an angle is a
length divided by another length so that these measurements are actually dimensionless and are
considered ‘pure’ numbers. For this reason, we do not use any symbols to denote radian measure,
but we use the word ‘radians’ to denote these dimensionless units as needed. For instance, we
say one revolution measures ‘2π radians,’ half of a revolution measures ‘π radians,’ and so forth.
As with degree measure, the distinction between the angle itself and its measure is often blurred
in practice, so when we write ‘θ = π ’, we mean θ is an angle which measures π radians.13 We
extend radian measure to oriented angles, just as we did with degrees beforehand, so...
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