Trigonometry & Analytical Geometry
Lab 1: Walker 225, 1/19/2007: 9-00 am. Quiz 1: January 22 at Regular classroom.Topics:
- A short course on Trigonometry
- On line help on Trigonometry
- Online Video Lessons-Trigonometry (Video)
- Distance, Midpoint Formulae, and Circles. [Do DVD->Worksheet number 8.]
- Quadratic Equations.
- Fractional expressions. (Go over the Fractional Equations under Algebra Boot Camp of your DVD).
- Lab Exercise (ClassPad file)
- 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?
- (Casio file).
- Higher Order Inequalities.
- Finding Domain of a function and Shifting
- Drills of finding domain of a function.
- Shifting and Reflection Techniques:
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).
- Practices on shifting, expansion and etc. (a PDF file). (**Hints/solutions)
- Extra Credits
- A CASIO file; a Maple worksheet.
- Composition of Functions
- Inverse functions
- More on inverse functions.
- (Skip this) Inverse functions
- Radians and Degrees (Reading materials)
- Sine Box (Java applet)
- Cosine Box (Java applet)
- Exercises on six trigonometric functions.
- Drawing a Sine function.
- Drawing a Cosine function.
[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)
- CASIO file on Sine and Cosine.
- CASIO file on Sine and Cosine Functions.
- Exercises (answer is on the same page).
- A flash about the unit circle.
- Pythagorean Theorem and etc.
- More on Trigonometric Functions
- About the
graphs of trig functions.
- Graph of y=tan(x) [Do you know how we get the graph?]
- (Skip) A Maple Exercise.
- 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.
- Modeling with Trigonometric Functions
- **Practice sheet for test 3-Spring 07 (Skip 4, 5, 6, and 7): Review for an old test
- (Skip) Maple Exercise
- **Practice sheet for test 3-Spring 07: Review for an old test.
- (Skip) Maple Exercise for Trigs and Inverse Trigs.
- Review for an old test 4.
- Review for an old test
- More on Trig. Subs.
- Review for an old Final.
- Extra Credits
- Java applets
- Center of gravity, stock car and trigonometry (discovered by Tommy Dickerson, a student of my Trig Spring 03)
- Interactive Algebra
- Test your knowledge on Trigonometry.
- ON LINE CALCULATOR.
- Maple Equation Solver,
- Some simple exercises with Maple.