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Homework Assignments

Spring 2008

Directions: Please follow these directions on all homework assignments.

1. It is recommended, but not required, that you do all of your homework on engineering graph paper (available in the bookstore).
2. On each homework assignment, place your name in the top right corner of the page.
3. On the first line of the of the first page of your homework, please write down the assignment number, the pages that encompass the assignement, and list each exercise number assigned. For example, the first line of your homework might read: Assignment #12, Page 150, #1, 3, 5, 7, 8, 10, 11, 23, 45
   
4. If an assignment takes more than a page, please staple the pages together with a single staple in the upper left-hand corner.
5. Simple one or two word answers or choices without explanatory prose are not acceptable. In all cases, use sound writing to justify your response.
6. Please do not do computation for a problem on one sheet of paper, then refer to a graph or diagram on another sheet of paper near the end of your stapled packet. Keep your work together, compuations and graphs and diagrams in the same general neighborhood on your homework.
7. Please do not crowd your work on your paper. Space things out and avoid tiny diagrams that are hard to read (please be nice to my old eyes).
8. Assignments will be handed in during classtime in separate piles: the assignment #1 pile, the assignment #2 pile, etc., so please do not staple two or more assignments together.

• Assignment #1
• • Log onto Web Advisor and make sure that your personal information (email, etc.) is up-to-date. It is absolutely essential that your email address in Blackboard and WebAdvisor is current. Read the Syllabus, then reply to the Welcome Message in the Math 120 Discussion Board in Blackboard saying that you have completed all of these tasks.
• Assignment #2
• • Start building your personal Math 25 Reference Book! Get a bound labbook with grid (graph) paper in it (the type used in chemistry or physics labs --- available in the bookstore). Make a title page with your name and contact information, set up a table of contents, and begin some entries (number the pages, with page #1 being the first page with information on it, after leaving a few pages blank for the table of contents to grow into).
    • Bring your Reference Book to the second class meeting on Tuesday and show me your title page, toc, and beginning page.
    • Throughout the semester, you should enter important information in your Reference Book, such as definitions, procedures, key examples, explanations that make sense to you, diagrams -- ANYTHING that you anticipate will be USEFUL to you as we proceed in this course ... and beyond! This is FOR YOU. In particular, your Reference Book should serve as a very useful study guide for quizzes and exams. (Note, however, that your Reference Book is not a substitute for class notes. In general, your Reference Book should be much more concise and organized than your class notes, which normally contain everything that we do in class.)
    • Each time we have an examination, I will collect your Reference Book and assign it a grade. In addition, although the final examination is closed book and closed notes, you will be allowed to use your Reference Book on the final exam.
• Assignment #3
• • Please read the following: http://msenux.redwoods.edu/IntAlgText/chapter9/section2.pdf
  • On http://msenux.redwoods.edu/IntAlgText/chapter9/section2exercises.pdf, do exercises #5, 6, 12, 13, 29, 30, 34, 35, 47, and 51.
• Assignment #4
• • Please read the following: http://msenux.redwoods.edu/IntAlgText/chapter9/section3.pdf
  • On http://msenux.redwoods.edu/IntAlgText/chapter9/section3exercises.pdf, do exercises #5, 6, 17, 18, 29, 30, 39, 45, and 46.
• Assignment #5
• • Please read the following: http://msenux.redwoods.edu/IntAlgText/chapter9/section4.pdf
  • On http://msenux.redwoods.edu/IntAlgText/chapter9/section4exercises.pdf, do exercises #31, 32, 49, 50, 55, 56, 57, 58, 61, and 66.
• Assignment #6
• • We will next undertake the study of geometry. You must take careful notes during class in order to undertake the exercises that follow.
  • Geometry has a rich history. Every serious mathematician should read the biography of Euclid. It is a fascinating story. The collection of Euclid's Elements can be read online. See: Elements
  • Download Geometry Exercises and do exercises #1, 3, 4, 5, 6, and 7.
  • Using only compass and straightedge (no marked ruler or protractor), start with a line AB and a point P not on the line, then construct a line through P that is perpendicular to the line AB. Use congruent triangles to argue that your construction is valid. That is, argue that your line through P is actually perpendicular to the line AB.
  • Some of you may want to get help in the Mathlab (Math 152) on these exercises. You should have a good set of detailed notes available for the tutors in the Mathlab to work with, otherwise, they might not be able to help.
• Assignment #7
• • You must have a detailed set of notes taken during class in order to undertake the exercises that follow.
  • Download Geometry Exercises and do exercises #8, 9, 10, 11, 12, and 13.
  • Some of you may want to get help in the Mathlab (Math 152) on these exercises. You should have a good set of detailed notes available for the tutors in the Mathlab to work with, otherwise, they might not be able to help.
• Optimath Quiz #1
• • Learn how to use Optimath at Introduction to Optimath.
  • Syntax use for Optimath is explained at Writing Mathematical Formulas in OPTIMATH.
  • Optimath Quiz #1 is due Monday, February 4, 11:50 pm.
• Assignment #8
• • Read Section 8.4 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, page 614 and following, do exercises #1, 10, 12, 15, 26, 29, 30, 36, 38, 44, 45, 46, 50, 54, 55, and 58.
• Assignment #9
  • Read Section 8.1 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, perform each of the following tasks:
    • On pages 576-577, do exercises #7, 8, 11, and 12. Include carefully labeled sketches with your solution.
    • Page 577, do exercises #22, 26, 30, 65, 68, 73, and 76. In each case, do not use DMS utility of your calculator. Rather, make the calculations from first prinicples, then use your calculator to find approximations.
    • Pages 579-581, do exercises #102, 103, 105, 113, 115, 118, 121, 124, 125, and 127. In each case, proceed as follows:
      • Provide a detailed and labeled sketch.
      • Solve the appropriate formula for the unknown variable. This might involve combining more than one formula.
      • Substitute known values into your resulting formula. Include units and show that they cancel to the desired final units.
      • State the solution with units.
• Assignment #10
  • Read Section 8.2 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, perform each of the following tasks:
    • On page 592, do exercises #3 and 8. Include carefully labeled sketches with your solution. See figures 27 and 28 in examples 1 and 2 in the reading.
    • Page 593, do exercises #30, 31, 32 and 33. Provide at least three example calculations from your calculator before stating your conjecture in both prose and mathematical symbols.
    • Page 594, do exercises #42, 44, and 45. In each case, start with the appropriate identity, make your substitution of known quantities, then solve. Place your final answer in simple radical form.
    • Page 594, do exercises #55, 58, 61, and 64. In each case, include a sketch of the required angle.
    • Page 594, do exercises #76, 77, and 78. In each case, state the appropriate identity, substitute known values, then solve. Place your answer in simple radical form. Follow the procedure outlined in Example 8 in the reading.
    • Page 595, do exercises #87, 88, and 90. In each case, provide a sketch similar to that in Figure 31 in Example 3. Place each answer in simple radical form.
    • Page 595, do exercises #93 and 96. In each case, start with the appropriate identity, then manipulate the identity algebraically to obtain the desired result. Follow the lead outlined in Example 9 in the reading.
• Download the Unit Circle
  • You can download a copy of the unit circle.
• Assignment #11
  • Read Section 8.3 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, perform each of the following tasks:
    • On page 604, use your unit circle to find exact values for the given trigonmetric expression in exercises #8, 10, 12, 14, 15, and 17.
    • Page 604, write each trigonometric function in exercises #23, 26, and 32 in terms of its cofunction expression.
    • Page 604, do exercises #34 and 43. In each case, sketch the given function and its reference angle on the same coordinate system.
    • Page 605-606, do exercises #81, 83, 86, 87, 90, 91, 95, and 96. In each case, sketch and label each angle solution on the same coordinate system.
    • Page 606, do exercise #111. Include a detailed, labeled sketch with your solution.
• Exam #1
  • You can downoad Exam #1, due Monday 2/25/08.
• Assignment #12
  • Read Section 8.5 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, page 626, do exercises #1-12, 13, 14, 15, 17, and 20.
• Optimath Quiz #2
  • Optimath Quiz #2 is posted. Due February 28, 11:50 pm.
• Assignment #13
  • Read Section 8.6 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, perform each of the following tasks. In each case, when asked to draw the graph of the function, clearly indicate the scale on each axis.
    • On page 642, state the amplitude and period of the function in exercises #31 and 38, then sketch the graph of the function on the interval [-2&pi, 2&pi] on graph paper.
    • On page 642, state the amplitude and period of the functions in exercises #39 and 44, then sketch the graph of the function over a two period interval of your choice on graph paper.
    • On page 642, state the amplitude, period, and phase shift of the functions in exercises #47 and 48, then sketch the graph of the function over a two period interval of your choice on graph paper.
    • On page 642, state the amplitude, period, and phase shift of the functions in exercises #51, 57, 58, and 65, then sketch the graph of the function over a one period interval of your choice on graph paper.
    • On page 644, make a copy the graph in exercise #80 on graph paper, then answer each of the question posed.
    • On page 644, answer each of the questions posed in exercise #82. When asked to sketch the graph, do so on graph paper.
    • On page 645, answer each of the questions posed exercise #86. Do any sketching on graph paper.
• Assignment #14
  • Read Section 8.7 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, on page 656, do exercises #23, 26, 32, 37, and 44. In each case, perform each of the following tasks:
    • State the period and phase shift (if any)
    • Sketch the graph over one period on graph paper. Draw the vertical asyptotes as dashed lines and label them with their equations. Clearly label the scale on each axis.
    • Use interval notation to describe the range of the function.
  • In A Graphical Approach to Algebra and Trigonometry, on page 656, do exercises #49, 50, and 52. In each case, perform each of the following tasks:
    • State the period and phase shift (if any)
    • Sketch the graph over two periods on graph paper. Draw the vertical asyptotes as dashed lines and label them with their equations. Clearly label the scale on each axis.
    • Use interval notation to describe the range of the function.
• Assignment #15
  • Read Section 8.8 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, on page 659, do exercises #1 and 4. In each case, perform each of the following tasks:
    • First, sketch at least one period of the graph of the model.
    • Answer parts (a) and (b).
  • In A Graphical Approach to Algebra and Trigonometry, on page 659-660, do exercises #9 and 12.
  • In A Graphical Approach to Algebra and Trigonometry, on page 660, do exercises #14, 16, and 17. In each case, sketch the graph of the motion.
  • In A Graphical Approach to Algebra and Trigonometry, on page 660, do exercises #19 and 20. In each case, use your graphing calculator to sketch the graph of the motion. Copy the image onto your homework paper.
• Optimath Quiz #3
  • Optimath Quiz #3 is up and due March 10, 11:50 pm. See http://msenux.redwoods.edu/optimath
• Assignment #16
  • Read Section 9.1 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, on pages 680-681, do exercises #23, 29, 40, 43, 44, 51, 55, 58, 59, and 60.
  • In A Graphical Approach to Algebra and Trigonometry, on page 682, prove the identities in exercises #74 79, 82, and 86. In each case, do not state as true the identity your are trying to prove in the first step of your proof. You must either:
    • Start with one side and through a series of steps show it is equal to the other side, or
    • Simplify the left-hand side, then simplify the right-hand side. If they both simplify to the same expression, write a concluding step that the left-hand side equals the right-hand side.
• Assignment #17
  • Again, read Section 9.1 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, on pages 681, do exercises #53, 54, 57, and 64.
  • In A Graphical Approach to Algebra and Trigonometry, on page 682, prove the identities in exercises #72, 73, 78, 80, 87, and 88. In each case, do not state as true the identity your are trying to prove in the first step of your proof. You must either:
    • Start with one side and through a series of steps show it is equal to the other side, or
    • Simplify the left-hand side, then simplify the right-hand side. If they both simplify to the same expression, write a concluding step that the left-hand side equals the right-hand side.
• Exam #2
  • You can downoad Exam #2, due Monday 3/10/08.
• Assignment #18
  • Again, read Section 9.2 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, on pages 690, do exercises #5, 10, 13, 18, 20, 21, 30, 32, and 35. Your work must show the use of the appropriate identity and all steps leading to the final answer.
  • In A Graphical Approach to Algebra and Trigonometry, on page 690, do exercises #43abef and #44cdef. You work must include two coordinate system, one showing angle A, the other angle B, each marked with angle, radial length, and a point with coordinates at the end of the radius. From this diagram you deduce the values of the trigonometric functions needed to complete the solution. Again, your work must start with the appropriate identity, use the results from your diagrams to fill in values of needed trigonometric functions, and your answers must be in simple radical form.
  • In A Graphical Approach to Algebra and Trigonometry, on page 690, prove the identities in exercises #47, 50, 53, and 54. In each case, do not state as true the identity your are trying to prove in the first step of your proof. You must either:
    • Start with one side and through a series of steps show it is equal to the other side, or
    • Simplify the left-hand side, then simplify the right-hand side. If they both simplify to the same expression, write a concluding step that the left-hand side equals the right-hand side.
• Assignment #19
  • Again, read Section 9.3 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, on pages 701, do exercises #1 and 4. In each case, provide a sketch with angle in the correct quadrant, select and endpoint at the end of the radius, then use your sketch and the appropriate identity to find the requested information in simple radical form.
  • In A Graphical Approach to Algebra and Trigonometry, on page 701, use the appropriate identity to simplify the given expression in exercises #7, 8, 16, 21, 24, 26, and 27. If needed, place your final answer in simple radical form.
  • In A Graphical Approach to Algebra and Trigonometry, on page 701, do exercises #31, 32, and 35. In each case, provide a sketch with angle in the correct quadrant, select and endpoint at the end of the radius, then use your sketch and the appropriate identity to find the requested information in simple radical form.
  • In A Graphical Approach to Algebra and Trigonometry, on page 702, do exercise #38. Provide detailed work for everything requested in the problem statement.
  • In A Graphical Approach to Algebra and Trigonometry, on page 702, prove the identities in exercises #47, 49, 52, and 54. In each case, do not state as true the identity your are trying to prove in the first step of your proof. You must either:
    • Start with one side and through a series of steps show it is equal to the other side, or
    • Simplify the left-hand side, then simplify the right-hand side. If they both simplify to the same expression, write a concluding step that the left-hand side equals the right-hand side.
  • In A Graphical Approach to Algebra and Trigonometry, on pages 702-703, use the appropriate identity to simplify the expressions in exercises #57, 58, 62, and 66.
• Assignment #20
  • Again, read Section 9.4 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, on pages 714, do exercises #7, 11, 12, 14, 16, 19, 27, 28, and 30. In each case, first copy the original problem onto your homework paper, then without the aid of a calculator, write down the answer.
  • In A Graphical Approach to Algebra and Trigonometry, on page 715, do exercises #35, 36, and 41. In each case, first copy down the problem, then use a calculator to estimate the answer.
  • In A Graphical Approach to Algebra and Trigonometry, on page 715, do exercises #57, 58, 61, 62, 63, and 68. In each case, first copy the original problem onto your homework paper, then without the aid of a calculator, write down the answer.
  • In A Graphical Approach to Algebra and Trigonometry, on page 715-716, do exercises #69, 70, 71, 73, 74, 76, 79, 82, 85, 93, 94, 99, and 100. Each solution must have an accopanying sketch, use the appropriate identity (if necessary), then capture the needed trigonometric values from your sketch. The sketch I am referring to in this case is the one we use for the trignometric function of any angle, the one that uses sin(theta) = y/r, cos(theta) = x/r, and tan(theta) = y/x.
• Exam #3
  • You can downoad Exam #3, due Monday 3/24/08.
• Optimath Quiz #4
  • Optimath Quiz #4 is up and due March 31, 11:50 pm. See http://msenux.redwoods.edu/optimath
• Assignment #21
  • Read Section 9.5 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, on pages 722, perform each of the following tasks for exercises #1, 2, and 6:
    1. On graph paper, by hand, sketch the graph of the left-hand side of each equation on the interval [0,2 π]. Shade and label the zeros of each function on the x-axis.
    2. Solve the equation analytically, finding exact answers and comparing with the zeros on your graph.
  • In A Graphical Approach to Algebra and Trigonometry, on page 722, find exact solutions for the equations in exercises #9, 11, 13, 18, 20, 21, and 24. Hand calculations only.
  • In A Graphical Approach to Algebra and Trigonometry, on page 722, perform each of the following tasks for exercises #25 and 26.
    1. Sketch the function on graph paper over the interval [0, 2 π).
    2. Find the exact zeros of the function analytically. Show your work. Shade and label the zeros of the function on the x-axis of your graph.
    3. Make a second copy of your plot on graph paper and shade and label the solution of f(x) > 0 on the x-axis.
    4. Make a third copy of your plot on graph paper and shade and label the solution of f(x) < 0 on teh x-axis.
  • In A Graphical Approach to Algebra and Trigonometry, on page 722, perform each of the following tasks for exercise #30 and 31:
    1. Use a graphing calculator to draw the graph of the given function, then make an accurate copy on your homework paper.
    2. Use the zero finding utility of your graphing calculator to estimate the zeros of the given function. Use an analytical technique to find the exact zeros, hand calculations only, and compare your results to the approximations found on the calculator. Shade and label these exact solutions on the x-axis of your plot.
    3. Make a second copy of the plot and shade and label the solution of f(x) > 0 on the x-axis of your plot. Use the exact zeros.
    4. Make a third copy of the plot and shade and label the solution of f(x) < 0 on the x-axis of your plot. Use the exact zeros.
  • In A Graphical Approach to Algebra and Trigonometry, on page 723, perform each of the following tasks for exercise #39 and 41:
    1. Use a graphing calculator to find approximate solutions. Make a copy of your final graph and mark your solutions on the graph.
    2. Use the quadratic formula to help find exact solutions. State the exact solutions over the given interval using inverse notation.
    3. Use your calculator to compare the exact solutions in part (2) with those found in part(1).
• Assignment #22
  • Read Section 9.6 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, on pages 728, perform each of the following tasks for exercises #3 and 8:
    1. On graph paper, by hand, sketch the graph of the left-hand side of each equation on the interval [0,2 π]. Sketch the right-hand side of each equation on the same plot. Solve the equation analytically, then drop dashed vertical lines from the points of intersection on your plot to the x-axis. Shade and label each solution of the equation on the x-axis.
    2. Redraw the plot a second time. Shade and label the solution to the inequality on the x-axis.
  • In A Graphical Approach to Algebra and Trigonometry, on page 728, find exact solutions for the equations in exercises #11, 12, 14, 15, 15, and 17. Hand calculations only.
  • In A Graphical Approach to Algebra and Trigonometry, on page 729, find exact solutions for the equations in exercises #25, 26, 29, and 30. Hand calculations only.
  • In A Graphical Approach to Algebra and Trigonometry, on pages 729-730, answer the questions posed in each part of exercises #41 and 43. Reproduce all calculator generated graphs on your homework paper and provide any hand calculations requested in the exercise.
• Assignment #23
• • Read Section 10.1 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, on pages 748, perform each of the following tasks for exercises #19 and 27:
    1. Use a protractor, compass, and ruler to draw a scale model of the given triangle. In each case, indicate the scale used on your diagram
    2. Use the law of sines to solve the given triangle. State each answer exactly using appropriate trigonometric notation (inverse notation, etc.), then use a calculator to find approximations.
  • In A Graphical Approach to Algebra and Trigonometry, perform each of the following tasks for exercises #31 and 33 on page 749:
    1. Use a protractor, compass, and ruler to draw a scale model of the given triangle. In each case, indicate the scale used on your diagram
    2. Use the law of sines to solve the given triangle. State each answer exactly using appropriate trigonometric notation (inverse notation, etc.), then use a calculator to find approximations.
  • In A Graphical Approach to Algebra and Trigonometry, on pages 750-752, do exercises #55, 57, 58, 60, 61, 63, 66, and 70. In each case, provide a detailed sketch.
• Optimath Quiz #5
• • Optimath quiz is up at http://msenux.redwoods.edu/optimath. Due Monday April 14, 11:50pm.
• Assignment #24
• • Read Section 10.2 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, on pages 761, perform each of the following tasks for exercises #19 and 23:
    1. Use a protractor, compass, and ruler to draw a scale model of the given triangle. In each case, indicate the scale used on your diagram
    2. Use the law of cosines to solve the given triangle. State each answer exactly using appropriate trigonometric notation (inverse notation, etc.), then use a calculator to find approximations.
  • In A Graphical Approach to Algebra and Trigonometry, on pages 761-7763, do exercises #43, 44, 46, 51, 52, 53, 54, and 55. In each case, provide a detailed sketch.
• Assignment #25
• • Read Section 10.3 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, on pages 775-776, do exercises #83, 87, 89, 91, 92, 101, 103, 105, and 107. In each case, use the technique of vector addition and provide a detailed sketch.
• Assignment #26
• • Read Section 10.4 in A Graphical Approach to Algebra and Trigonometry. Important Note: I will be presenting a far superior notation for complex numbers in trigonometric form using Euler's Identity: r e^iθ = r (cos θ - i sin θ)
  • In A Graphical Approach to Algebra and Trigonometry, on page 785, perform each of the following tasks for exercises #21, 25, and 26:
    1. Sketch the given number in the complex plane, and
    2. calculate the modulus or length of the complex number.
  • In A Graphical Approach to Algebra and Trigonometry, on page 785, perform each of the following tasks for exercises #29, 36, and 38:
    1. Sketch the given number in the complex plane, and
    2. Using pencil and paper calculations, place the given complex number in rectangular form.
  • In A Graphical Approach to Algebra and Trigonometry, on page 785, perform each of the following tasks for exercises #41, 45, 49, and 51:
    1. Sketch the given number in the complex plane, and
    2. Using pencil and paper calculations, place the given complex number in trigonometric form.
    3. Using pencil and paper calculations, place the given complex number in the form r e^iθ = r (cos θ - i sin θ)
  • In A Graphical Approach to Algebra and Trigonometry, on page 785, perform each of the following tasks for exercises #33, 59, and 60:
    1. Sketch each given number and the product of the two complex numbers in the complex plane. Label each complex number with its value.
    2. Using pencil and paper calculations, compute the product of the given complex numbers, placing your product in the form: r e^iθ = r (cos θ - i sin θ)
  • In A Graphical Approach to Algebra and Trigonometry, on page 785, perform each of the following tasks for exercises #61 and 63:
    1. Sketch each given number and the product of the two complex numbers in the complex plane. Label each complex number with its value.
    2. Using pencil and paper calculations, compute the product of the given complex numbers, placing your product in the form: r e^iθ = r (cos θ - i sin θ)
• Optimath Quiz #6
  • Optimath Quiz #6 is due Monday, April 28, 11:50 pm. It is available on Optimath.
• Assignment #27
• • Read Section 10.5 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, on page 791, do exercises #10, 11, 13, 14, 15, and 18. Use the technique shown in class that uses e^iθ.
  • On page 791, do exercises #19, 20, 25, 26, and 27. Use the technique shown in class that uses e^iθ. In each exercise, sketch the solutions in the complex plane.
  • On page 791, do exercises #33, 36, 38, and 40. Use the technique shown in class that uses e^iθ.
• Exam #5
  • You can downoad Exam #5. It is due Monday, 4/28, at the beginning of class.
• Assignment #28
• • Read Section 6.1 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, on pages 428-429, do exercises #11, 17, 19, and 35 without the aid of a calculator. Provide a sketch on graph paper.
  • On page 429, complete the square for exercises #41, 42, 45, and 46, then sketch the ellipse on graph paper.
  • On page 430, do exercises #63, 70, 71, 82, and 83 without the aid of a calculator. Provide a sketch on graph paper and label vertex and focus with coordinates, directric with its equation.
  • On page 430, complete the square in exercise #105 and 107, then sketch the result on graph paper. Label the vertex, focus, and directrix.
• Assignment #29
• • Read Section 6.2 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, on pages 441, do exercises #13, 17, 23, 24, 29, and 33 without the aid of a calculator. Provide a sketch on graph paper. In each case, label vertices and foci with their coordinates.
  • On page 442, complete the square for exercises #23, 24, 29, and 33, then sketch the ellipse on graph paper. Label vertices and foci with coordinates.
  • On page 442-443, do exercises #49, 57, 62, and 65 without the aid of a calculator. Provide a sketch on graph paper. Label vertices and foci with coordinates. Draw your box and label the asymptotes with their equations.
  • On page 443, complete the square in exercises #71, 72, and 74, then sketch the result on graph paper. Label the vertices and foci with coordinates. Draw your box and label your asymptotes with their equations.
• Assignment #30
• • Read Section 10.6 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, on pages 801, do exercise #33 on polar graph paper. The expectation is that you calculate points on your calculator, then plot them carefully on polar graph paper.
  • On page 801, use the shortcuts presented in class to sketch the polar curves in exercises #35, 37, and 39 without the use of polar graph paper or a calculator. You may use your calculator to check your result, but you may not use your calculator to produce the graph. You must do the work without the calculator.
  • On pages 802-803, in exercises #55, 57, 59, 61, and 63, change the polar equations to cartesian equations and graph the result on cartesian graph paper. Again, you may use your calculator to check your result, but you may not use your calculator to produce the graph.
• Assignment #31
• • Read Section 10.7 in A Graphical Approach to Algebra and Trigonometry
  • In A Graphical Approach to Algebra and Trigonometry, on page 809, do exercises #17, 19, 20, and 21. Use your calculator to produce the parametric plot, then transpose the result to graph paper.
  • On page 810, use your calculator to produce the Lissajous curves presented in exercises #33 and 35. Transpose your result onto graph paper.