Trigonometry & Analytical Geometry
Lab 1: Walker 225, 1/19/2007: 900 am. Quiz 1: January 22 at Regular classroom.
Topics: A short course on Trigonometry
 On line help on Trigonometry
 Online Video LessonsTrigonometry (Video)
 Distance, Midpoint Formulae, and Circles. [Do DVD>Worksheet number 8.]
 Factoring
 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 breakeven point.
(d) Find the total weekly revenue at the breakeven point.  Check your notes for CF 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:
 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).
 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
 (Maple worksheet).
 Exercises. (a MS Word document).
 Radians
and Degrees (Reading materials)
 Radians and Degrees (A video)
 Reference Angle (A video)
 Do the exercises on Radian Measure and Angles.
 Sine Box (Java applet)
 Cosine Box (Java applet)
 Exercises on six trigonometric functions.
 Drawing a Sine function.
 Drawing a Cosine function.
 **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)
 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 3Spring 07 (Skip 4, 5, 6, and 7): Review for an old test
 (Skip) Maple Exercise
 **Practice sheet for test 3Spring 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

Trigonometric substitutions.
 More on Trig. Subs.
 Review for an old Final.
 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.
 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.