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Unformatted text preview: of the Trigonometric Functions In this section, we return to our discussion of the circular functions as functions of real numbers
and pick up where we left oﬀ in Sections 10.2.1 and 10.3.1. As usual, we begin our study with the
functions f (t) = cos(t) and g (t) = sin(t). 10.5.1 Graphs of the Cosine and Sine Functions From Theorem 10.5 in Section 10.2.1, we know that the domain of f (t) = cos(t) and of g (t) = sin(t)
is all real numbers, (−∞, ∞), and the range of both functions is [−1, 1]. The Even / Odd Identities
in Theorem 10.12 tell us cos(−t) = cos(t) for all real numbers t and sin(−t) = − sin(t) for all real
numbers t. This means f (t) = cos(t) is an even function, while g (t) = sin(t) is an odd function.1
Another important property of these functions is that for coterminal angles α and β , cos(α) = cos(β )
and sin(α) = sin(β ). Said diﬀerently, cos(t + 2π · k ) = cos(t) and sin(t + 2π · k ) = sin(t) for all real
numbers t and any integer k . This last property is given a specia...
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