Unformatted text preview: numbers by identifying a real number t with the angle θ = t radians. Using this identiﬁcation, we
deﬁne cos(t) = cos(θ) and sin(t) = sin(θ). In practice this means expressions like cos(π ) and sin(2)
can be found by regarding the inputs as angles in radian measure or real numbers; the choice is
the reader’s. If we trace the identiﬁcation of real numbers t with angles θ in radian measure to its
roots on page 604, we can spell out this correspondence more precisely. For each real number t, we
associate an oriented arc t units in length with initial point (1, 0) and endpoint P (cos(t), sin(t)).
y y 1 1 P (cos(t), sin(t)) t
1 x 1 x In the same way we studied polynomial, rational, exponential, and logarithmic functions, we will
study the trigonometric functions f (t) = cos(t) and g (t) = sin(t). The ﬁrst order of business is to
ﬁnd the domains and ranges of these functions. Whether we think of identifying the real number
t with the angle θ = t radians, or think of wrap...
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