College Trigonometry, 2011a

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894 Applications of <strong>Trigonometry</strong> 11.1.3 Answers 1. S(t) = sin (880πt) 2. V (t) = 220 √ 2 sin (120πt) 3. h(t) =67.5sin ( π 15 t − π ) 2 +67.5 ( 4. x(t) =67.5cos π 15 t − π ) ( 2 =67.5sin π 15 t) 5. h(t) = 28 sin ( 2π 3 t − π ) 2 +30 6. (a) k =5 lbs. ft. and m = 5 16 slugs (b) x(t) =sin ( 4t + π ) 2 . The object first passes through the equilibrium point when t = π 8 ≈ 0.39 seconds after the motion starts. At this time, the object is heading upwards. √ (c) x(t) = 2 2 sin ( 4t + 7π ) 4 . The object passes through the equilibrium point heading downwards for the third time when t = 17π 16 ≈ 3.34 seconds. (√ ) 7. (a) θ(t) =θ 0 sin g l t + π (b) θ(t) = π 2 12 sin ( 4πt + π ) 2 8. (a) T (t) =20.5sin ( π 6 t − π) +53.5 (b) Our function and the data set are graphed below. The sinusoid seems to be shifted to the right of our data. (c) The average temperature on April 15 th is approximately T (4.5) ≈ 39.00 ◦ Fandthe average temperature on September 15 th is approximately T (9.5) ≈ 73.38 ◦ F. (d) Using a graphing calculator, we get the following This model predicts the average temperature for April 15 th to be approximately 42.43 ◦ F and the average temperature on September 15 th to be approximately 70.05 ◦ F. This model appears to be more accurate.
11.1 Applications of Sinusoids 895 9. (a) Based on the shape of the data, we either choose A
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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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Page 197 and 198: Chapter 11 Applications of Trigonom
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11.5 Graphs of Polar Equations 945
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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 977 The
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11.6 Hooked on Conics Again 979 We
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11.6 Hooked on Conics Again 983 The
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11.6 Hooked on Conics Again 985 In
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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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11.8 Vectors 1013 Q ′ (1, 7) up 4
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11.8 Vectors 1015 ⃗v + ⃗w = 〈
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11.8 Vectors 1017 ⃗v − ⃗w =
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11.8 Vectors 1019 The remaining pro
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11.8 Vectors 1021 ‖k⃗v‖ = ‖
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11.8 Vectors 1023 at the origin, th
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11.8 Vectors 1025 Geometrically, th
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11.8 Vectors 1027 11.8.1 Exercises
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11.8 Vectors 1029 44. ⃗v = 〈−
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11.8 Vectors 1031 11.8.2 Answers 1.
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11.8 Vectors 1033 47. ‖⃗v‖ =2
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11.9 The Dot Product and Projection
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11.10 Parametric Equations 1049 obj
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11.10 Parametric Equations 1051 2.
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11.10 Parametric Equations 1053 Now
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11.10 Parametric Equations 1057 Our
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11.10 Parametric Equations 1061 Sup
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Index n th root of a complex number
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Index 1071 central angle, 701 chang
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Index 1073 reflective property, 523
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Index 1075 matrix, multiplicative,
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Index 1077 midpoint definition of,
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Index 1079 instantaneous, 161, 472
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Index 1081 inconsistent, 553 indepe
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College Trigonometry, 2011a

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