Unformatted text preview: terminal, cos(θ) = cos(θ0 ) and sin(θ) = sin(θ0 ).
y y 1 1 θ0 θ0
P (cos(θ0 ), sin(θ0 )) θ 1 x Q(cos(−θ0 ), sin(−θ0 )) 1 x − θ0 We now consider the angles −θ and −θ0 . Since θ is coterminal with θ0 , there is some integer k so
that θ = θ0 + 2π · k . Therefore, −θ = −θ0 − 2π · k = −θ0 + 2π · (−k ). Since k is an integer, so is
(−k ), which means −θ is coterminal with −θ0 . Hence, cos(−θ) = cos(−θ0 ) and sin(−θ) = sin(−θ0 ).
Let P and Q denote the points on the terminal sides of θ0 and −θ0 , respectively, which lie on the
Unit Circle. By deﬁnition, the coordinates of P are (cos(θ0 ), sin(θ0 )) and the coordinates of Q are
(cos(−θ0 ), sin(−θ0 )). Since θ0 and −θ0 sweep out congruent central sectors of the Unit Circle, it
follows that the points P and Q are symmetric about the x-axis. Thus, cos(−θ0 ) = cos(θ0 ) and
As mentioned at the end of Section 10.2, properties of the circular functions when thought of as functions of
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