Stitz-Zeager_College_Algebra_e-book

16 to the case when we obtain the following double

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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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