Unformatted text preview: y ) x r θ
O A(x , 0) B (x, 0) x Not only can we describe the coordinates of Q in terms of cos(θ) and sin(θ) but since the radius of
the circle is r = x2 + y 2 , we can also express cos(θ) and sin(θ) in terms of the coordinates of Q.
These results are summarized in the following theorem.
Theorem 10.3. Suppose Q(x, y ) is the point on the terminal side of an angle θ, plotted in standard
position, which lies on the circle of radius r, x2 + y 2 = r2 . Then x = r cos(θ) and y = r sin(θ).
Moreover,
cos(θ) =
10 Do you remember why? x
=
r x
x2 + y2 and sin(θ) = y
=
r y
x2 + y2 626 Foundations of Trigonometry Note that in the case of the Unit Circle we have r =
our deﬁnitions of cos(θ) and sin(θ). x2 + y 2 = 1, so Theorem 10.3 reduces to Example 10.2.6.
1. Suppose that the terminal side of an angle θ, when plotted in standard position, contains the
point Q(4, −2). Find sin(θ) and cos(θ).
2. In Example 10.1.5 in Section 10.1, we approximated the radius of the earth at 41.628◦...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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