Professor Wei-Chi Yang

• On Sabbatical Leave-Fall 2006.
• Spring 07 Schedule
• Professional Activities
• Education
• Teaching Experiences
• Founder, ATCM
• Curriculum Vitae

Remember:

Be sure to get all your homework done as soon as possible after class as this will lead to better grades.

Links:

- RU
- My book mark
- ATCM
- E-mail Me

Walker 203; Phone: (540) 831-5232

Trigonometry & Analytical Geometry

Course Contract

Lab 1: Walker 225, 1/19/2007: 9-00 am. Quiz 1: January 22 at Regular classroom.

1. A short course on Trigonometry
2. On line help on Trigonometry
3. Online Video Lessons-Trigonometry (Video)
4. Distance, Midpoint Formulae, and Circles.  [Do DVD->Worksheet number 8.]
   • Pythagorean Theorem (1)
   • Pythagorean Theorem (2)
5. Factoring
   • Practices on factorings
6. Quadratic Equations.
   • More exercises on Quadratic Equations.
7. Fractional expressions. (Go over the Fractional Equations under Algebra Boot Camp of your DVD).
8. Lab Exercise (ClassPad file)
9. Line equations
   • Exercise 1: You are about to take a trip and you plan to rent a car, here are two rental offers: (i) Hertz will give you 30 cents per mile and $45 per day, and (ii) Avis will give you 25 cents per mile and $50 per day. Suppose you decide to rent a car for 4 days. Which company offers you a better deal? Explain. Answer.
   • Exercise 2: A manufacturer of electronic components finds that in making x units of a prduct weekly it has a cost of $2 per unit, plus a fixed cost of $1800. Each unit sells for $5.
     (a) Find the cost, revenue and profit functions.
     (b) Sketch these functions.
     (c) Find the break-even point.
     (d) Find the total weekly revenue at the break-even point.
   • Check your notes for C-F problems: Do you know Celsius would meet Fahrenheit at some point? Where?
10. (Casio file).
    • Practice problem set 1.
11. Higher Order Inequalities.
12. Finding Domain of a function and Shifting
13. Drills of finding domain of a function.
14. Shifting and Reflection Techniques:
    • Practices on shifting, expansion and etc. (a PDF file). (**Hints/solutions)
      • Horizontal Shifting: y = f(x + a) is a horizontal shifting of y = f(x). If a > 0, then the graph will be shifted to the left; if a <0, then the graph will be shifted to the right.
      • Vertical Shifting: y = f(x) + a is a vertical shifting of y = f(x). If a > 0, then the graph will be shifted up; if a <0, then the graph will be shifted down.
      • y = - f(x) is a reflection of y = f(x).
      • A Maple worksheet.
      • A Java Applet.
15. Extra Credits
16. A CASIO file;  a Maple worksheet.
17. Composition of Functions
    • Drill
18. Inverse functions
    • Drill.
19. More on inverse functions.
    • Practice on composite and inverse functions.
    • Solution is here.
20. (Skip this) Inverse functions
    • (Maple worksheet).
    • Exercises. (a MS Word document).
21. Radians and Degrees (Reading materials)
    • Radians and Degrees (A video)
    • Reference Angle (A video)
    • Do the exercises on Radian Measure and Angles.
22. Sine Box (Java applet)
    • Reading and exercises for Sines.
23. Cosine Box (Java applet)
    • Reading and exercises for Cosines.
24. Exercises on six trigonometric functions.
25. Drawing a Sine function.
26. Drawing a Cosine function.
27. **Exercises [Prepare these for the quiz on March 23]
    • Do 4,5,8 Review sheet for an old test
    • More exercises on finding six trigonometric values. (answer here)
28. CASIO file on Sine and Cosine.
29. CASIO file on Sine and Cosine Functions.
30. Exercises (answer is on the same page).
31. A flash about the unit circle.
32. Pythagorean Theorem and etc.
33. More on Trigonometric Functions
34. About the graphs of trig functions.
    • Graph of y=tan(x) [Do you know how we get the graph?]
35. (Skip) A Maple Exercise.
36. Define the function f whose graph is similar to a "sine" function and satisfies the following conditions 
    • The period of f is 180 degree.
    • The function f has the amplitude of 3.
    • The function f has the highest value of 0 at x=135 degree.
37. Modeling with Trigonometric Functions
38. **Practice sheet for test 3-Spring 07 (Skip 4, 5, 6, and 7): Review for an old test 
39. (Skip) Maple Exercise
40. **Practice sheet for test 3-Spring 07: Review for an old test.
41. (Skip) Maple Exercise for Trigs and Inverse Trigs.
42. Review for an old test 4.
43. Review for an old test
44. Trigonometric substitutions.
    • More on Trig. Subs.
45. Review for an old Final.
46. Extra Credits
    • Try to explain why Ferris Wheel is related to trigonometric functions.
    • Figure out the height of the pole.
    • Figure out the angle.
    • Another angle problem.

1. Java applets
2. Center of gravity, stock car and trigonometry (discovered by  Tommy Dickerson, a student of my Trig Spring 03)
   • It talks about how to find the center of gravity and has a program. 
   • It talks about the center of gravity height and Jeeps, and the danger of them
     flipping.
   • Very informative site about the center of gravity height
      
3. Interactive Algebra
4. Test your knowledge on Trigonometry.
5. ON LINE CALCULATOR.
6. Maple Equation Solver,
7. Some simple exercises with Maple.
   • Arithmetic with Maple
   • Creating Graphs in Maple

Copyright © 2006 (Wei-Chi Yang).