College Trigonometry, 2011a

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1052 Applications of <strong>Trigonometry</strong> positive y-coordinates. To better explain this behavior, we eliminate the parameter. Using a reciprocal identity, we write y = csc(t) = 1 sin(t) .Sincex =sin(t), the curve traced out by this parametrization is a portion of the graph of y = 1 x . We now can explain the unusual behavior as t → 0 + and t → π − – for these values of t, we are hugging the vertical asymptote x =0of the graph of y = 1 x . We see that the parametrization given above traces out the portion of y = 1 x for 0
11.10 Parametric Equations 1053 Now that we have had some good practice sketching the graphs of parametric equations, we turn to the problem of finding parametric representations of curves. We start with the following. Parametrizations of Common Curves ˆ To parametrize y = f(x) asx runs through some interval I, letx = t and y = f(t) andlet t run through I. ˆ To parametrize x = g(y) asy runs through some interval I, letx = g(t) andy = t and let t run through I. ˆ To parametrize a directed line segment with initial point (x 0 ,y 0 ) and terminal point (x 1 ,y 1 ), let x = x 0 +(x 1 − x 0 )t and y = y 0 +(y 1 − y 0 )t for 0 ≤ t ≤ 1. ˆ To parametrize (x−h)2 + (y−k)2 =1wherea, b > 0, let x = h + a cos(t) andy = k + b sin(t) a 2 b 2 for 0 ≤ t
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College Trigonometry Version ⌊π
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Table of Contents vii 10 Foundation
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Preface Thank you for your interest
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xi text and we have gone to great l
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Chapter 10 Foundations of Trigonome
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10.1 Angles and their Measure 695 k
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10.1 Angles and their Measure 697 2
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10.1 Angles and their Measure 701 T
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10.1 Angles and their Measure 703 y
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10.1 Angles and their Measure 705 y
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10.1 Angles and their Measure 707 h
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10.1 Angles and their Measure 711 I
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10.2 The Unit Circle: Cosine and Si
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30 ◦ 1 10.2 The Unit Circle: Cosi
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10.3 The Six Circular Functions and
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10.4 Trigonometric Identities 771 f
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10.4 Trigonometric Identities 773 2
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10.4 Trigonometric Identities 779 T
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10.4 Trigonometric Identities 781 R
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10.4 Trigonometric Identities 785 I
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10.5 Graphs of the Trigonometric Fu
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10.6 The Inverse Trigonometric Func
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10.7 Trigonometric Equations and In
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Chapter 11 Applications of Trigonom
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11.1 Applications of Sinusoids 883
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11.2 The Law of Sines 897 minimizes
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11.2 The Law of Sines 899 a angle-s
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11.2 The Law of Sines 901 determine
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11.2 The Law of Sines 903 Let x den
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11.2 The Law of Sines 905 24. Along
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11.2 The Law of Sines 907 33. The a
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11.2 The Law of Sines 909 25. (a)
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11.3 The Law of Cosines 911 of B ar
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11.3 The Law of Cosines 913 the pre
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11.3 The Law of Cosines 915 A 2 = =
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11.3 The Law of Cosines 917 22. A n
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11.4 Polar Coordinates 919 11.4 Pol
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11.4 Polar Coordinates 921 The poin
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11.4 Polar Coordinates 923 4. We mo
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11.4 Polar Coordinates 925 Solution
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11.4 Polar Coordinates 927 Solution
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11.4 Polar Coordinates 929 algebrai
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11.4 Polar Coordinates 931 45. ( )
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11.4 Polar Coordinates 933 5. ( 12,
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11.4 Polar Coordinates 935 13. (
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11.4 Polar Coordinates 937 73. r =7
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11.5 Graphs of Polar Equations 939
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11.6 Hooked on Conics Again 973 11.
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11.6 Hooked on Conics Again 975 Exa
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11.6 Hooked on Conics Again 983 The
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11.6 Hooked on Conics Again 989 2 9
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11.7 Polar Form of Complex Numbers
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College Trigonometry, 2011a

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