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C-6 Appendix C MINI PROJECT Thinking About Symmetry This mini project works well in the context of a small group discussion but, of course, it can also be carried out by individuals. Begin by studying and/or discussing the following example involving a regular hexagon. Then work on the exercise that follows. For each part of the exercise, label each figure that you create (for example, “symmetric about the y-axis, but not the x-axis”). Example: The following figure shows a regular hexagon. The next four figures show some of the (infinitely many) ways to locate the regular hexagon with respect to an x-y coordinate system. y y x x (a) Symmetric about y-axis, but not about x-axis (b) Symmetric about x-axis, but not about y-axis y y x x (c) Symmetric about origin and about both axes (d) Symmetric about origin and not about either axis In each case below, you are given a geometric figure. Try to find a way to draw the figure with an x-y coordinate system so that the figure is (a) symmetric about the y-axis, but not about the x-axis; (b) symmetric about the x-axis, but not about the y-axis; (c) symmetric about the origin and both axes; (d) symmetric about the origin but not about either axis. (In some cases there are many ways, in others none.)
Appendix C C-7 1. equilateral triangle: 2. rectangle: 3. regular pentagon: 4. semicircle: 5. connected semicircles:
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Page 3 and 4: Appendix C C-3 MINI PROJECT Discuss
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Page 9 and 10: Appendix C C-9 MINI PROJECT Flying
Page 11 and 12: Appendix C C-11 MINI PROJECT An Ine
Page 13 and 14: Appendix C C-13 (a) The two data po
Page 15 and 16: Appendix C C-15 and http://www.svob
Page 17 and 18: Appendix C C-17 For Figure D we can
Page 19 and 20: Appendix C C-19 MINI PROJECT A Grap
Page 21 and 22: Appendix C C-21 MINI PROJECT Who Ar
Page 23 and 24: Appendix C C-23 MINI PROJECT 1 How
Page 25 and 26: Appendix C C-25 either the quadrati
Page 27 and 28: Appendix C C-27 PROJECT The Least-S
Page 29 and 30: Appendix C C-29 Then, for any line
Page 31 and 32: Appendix C C-31 PROJECT Finding Som
Page 33 and 34: Appendix C C-33 3. When a person co
Page 35 and 36: Appendix C C-35 2. Use part (b) of
Page 37 and 38: Appendix C C-37 PROJECT Coffee Temp
Page 39 and 40: Appendix C C-39 MINI PROJECT More C
Page 41 and 42: Appendix C C-41 The calculations co
Page 43 and 44: Appendix C C-43 PROJECT Transits of
Page 45 and 46: Appendix C C-45 E A ¨ V ¨ Bª d S
Page 47 and 48: Appendix C C-47 PROJECT A Linear Ap
Page 49 and 50: Appendix C C-49 Continuing with the
Page 51 and 52: Appendix C C-51 PROJECT Constructin
Page 53 and 54: Appendix C C-53 1 y Figure A A grap
Page 55 and 56: Appendix C C-55 PROJECT Fourier Ser
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Appendix C C-57 sine and cosine fun
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Appendix C C-59 PROJECT The Motion
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Appendix C C-61 PROJECT The Design
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Appendix C C-63 denote the angles o
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Appendix C C-65 inverse trigonometr
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Appendix C C-67 PROJECT Inverse Sec
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Appendix C C-69 Alternatively, usin
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Appendix C C-71 PROJECT Snell’s L
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Appendix C C-73 vertically downward
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0 0 0 Appendix C C-75 PROJECT Vecto
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Appendix C C-77 Exercise 8 We outli
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Appendix C C-79 y y=2x+5 Îy=2 A (1
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 Appendi
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Appendix C C-83 PROJECT Parameteriz
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Appendix C C-85 It is worth noting
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Appendix C C-87 6. Show that the li
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Appendix C C-89 2. An altitude of a
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Appendix C C-91 PROJECT The Leontie
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Appendix C C-93 n x units of that
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Appendix C C-95 him/herself through
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Appendix C C-97 PROJECT The Leontie
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Appendix C C-99 As in the solution
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Appendix C C-101 MINI PROJECT 2 Con
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Appendix C C-103 PROJECT Using Hype
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Appendix C C-105 PROJECT Two Method
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Appendix C C-107 (b) Use Method 1 t
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Appendix C C-109 MINI PROJECT An Un
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Appendix C C-111 PROJECT More on Su
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Appendix C C-113 SOLUTION 25 25 a (
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Appendix C C-115 4. Simplify the fo
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