College Trigonometry, 2011a

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1058 Applications of <strong>Trigonometry</strong> it seems reasonable to keep these as our bounds on t. The ‘Tstep’ seems reasonably small – too large a value here can lead to incorrect graphs. 14 We know from our derivation of the equations of the cycloid that the center of the generating circle has coordinates (rθ, r), or in this case, (3t, 3). Since t ranges between 0 and 2π, we set x to range between 0 and 6π. Thevaluesofy go from the bottom of the circle to the top, so y ranges between 0 and 6. Below we graph the cycloid with these settings, and then extend t to range from 0 to 6π which forces x to range from 0 to 18π yielding three arches of the cycloid. (It is instructive to note that keeping the y settings between 0 and 6 messes up the geometry of the cycloid. The reader is invited to use the Zoom Square feature on the graphing calculator to see what window gives a true geometric perspective of the three arches.) 14 Again, see page 959 in Section 11.5.
11.10 Parametric Equations 1059 11.10.1 Exercises In Exercises 1 - 20, plot the set of parametric equations by hand. Be sure to indicate the orientation imparted on the curve by the parametrization. 1. { { x =4t − 3 x =4t − 1 y =6t − 2 for 0 ≤ t ≤ 1 2. y =3− 4t for 0 ≤ t ≤ 1 3. 5. { x =2t y = t 2 for − 1 ≤ t ≤ 2 4. { x = t 2 +2t +1 y = t +1 for t ≤ 1 6. { x = t − 1 y =3+2t − t 2 for 0 ≤ t ≤ 3 { ( x = 1 9 18 − t 2 ) y = 1 3 t for t ≥−3 7. { x = t y = t 3 for −∞
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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 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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