113 fall 2000 course outline

MTH 113 COURSE OUTLINE Fall 2000

INSTRUCTOR: K.W.NICHOLSON OFFICE HOURS: POSTED ON DOOR OF RM 224.

TEXT: Barnett, Ziegler & Byleen's PRE CALCULUS, Functions and Graphs, Fourth Ed

CONTENT:

Chap 5 - Trig Functions
Chap 6- Trig Identities and Conditional Equations
Chap 7 - Law of sins, cosines, vectors, and complex numbers

Message from the instructor:

Everyone is always wanting to feel that there is some practical use of the math they learn. Up to now this has been a little difficult to do. Algebra is like the support team that makes the really glitzy math possible. But again, to be able to use most of the glitzy stuff requires additional knowledge of physics, chemistry, statistics, or some such field as that. Trigonometry enables us to solve simple geometry situations, and even delve intuitively into some physical applications of math that literally reach all the way to the stars. This makes it the most easily accessible of the "glitzy" math. I think you'll really enjoy it. These examples of uses come primarily from right triangle trigonometry, which makes up part of this course. We must also, however, delve into the more formal side of trig, studying trigonometric functions. These help to make calculus and physics more powerful and useful. Although the study of trig functions may not be quite as glitzy, it ultimately yields much more fruit than right triangle trig. If you keep this in mind, this entire course should be both exciting and fascinating. kwn.

EVALUATION:

Item

Date

Discussion

3-100 point tests

Sept. 7, Oct. 5, and Nov. 2

No make up tests will be given. A missed test will be replaced by 1/2 of your final exam score.

Note: Online students unable to take the tests in class, may take them in the physics lab BS 214 Wed, Thur, or Fri, of that week, 12 - 5 PM.

1-200 point Final Exam

Dec. 7

Final will be comprehensive.

Online homework- 200 points

Tuesday's homework is due at midnight the next night, Wednesday. Thursday's homework is due at midnight the following Monday.

Homework problems will given one point each, but your final score will be divided by the total possible and multiplied by 200.

The Thinkwell website provides hints for most of the problems in case you get stuck. But there will also be online discussion sessions every Tuesday and Thursday evenings 6 - 8 pm. You may also obtain assistance via email.

GRADES:

The accumulative total for the course will be 700 points and your accumulative total will be divided by that amount to calculate your final average.

90 - 100 = A, 80 - 89 = B, 70 - 79 = C, 60 - 69 = D, 0 - 59 = F

NOTES:
l. Final percentage will be rounded UP, i.e., a final percent of 79.00000001 will be rounded up to 80.
2. You should keep all returned papers. You should also keep track of the ratio (your accumulative total)/(The accumulative total possible to date) as the quarter progresses. If this ratio is below 70 at midterm (October 13, 2000), you should come for a conference with the instructor to discuss what each of us can do to retrieve you from doom.
3. If you have more than two excused absences you will be dropped from the course, as required by the college admission policies.

4. Words of wisdom regarding Math homework.

I hear........ and I forget,
I see..........and I remember,
I do...........and I understand.

Course Overview

You may take this course either online or in class, or a combination of the two. Here's how it works.

I will deliver the lectures in the table below on the specified dates. Each lecture will have a corresponding textbook homework and online homework. Textbook homework will not be turned in. We will discuss those in class and online.

The online homework will be for credit, it will be submitted online and graded automatically. There will be an online discussion session for those with questions or comments about the homework assignment on Tuesday and Thursday evenings from 6 to 8 PM. Other discussions will be hosted by students in this class and announced on the web site once they are organized. Homework assignments are due Wednesday and Monday nights at midnight.

Note: Online students unable to take the tests in class, may take them in the physics lab BS 214 Wed, Thur, or Fri, of that week, 12 - 5 PM.

The Thinkwell packet you purchased at the bookstore includes three CD's. The same set of lectures that I am giving are on these CD's, only they are done by Dr. Edward Burger.

THE BIG PICTURE

Class time: 8:00 - 9:15 Tuesday and Thursday .

DAILY SCHEDULE

Date

Topic / Thinkwell Assignments

B, Z, & B's hwk problems

8- 22

Angles and Radian Measure
• Finding the Quadrant in Which an Angle Lies
• Finding Coterminal Angles
• Finding the Complement and Supplement of an Angle
• Converting Between Degrees and Radians
• Using the Arc Length Formula

• Orientation to Math 113 Web page
• Log onto Thinkwell and do first homework assignment
• Log onto Blackboard and join a discussion session.

Pg. 364: 1,3,7,9,11,13,17,19,21,67, 69,73,75

8-24

Right Angle Trigonometry
An Introduction to the Trigonometric Functions
• Finding an Angle Given the Value of a Trigonometric Function
• Using Trigonometric Functions to Find Unknown Sides of Right Triangles
• Finding the Height of a Building

pg. 381: 5,9, 55,58

8-29

The Trigonometric Functions
• Evaluating Trigonometric Functions for an Angle in the Coordinate Plane
• Evaluating Trigonometric Functions Using the Reference Angle
• Finding the Value of Trigonometric Functions Given Information About the Values of Other Trig Functions
• Trigonometric Functions of Important Angles

pg. 381: 33,37,45,61,63

pg. 381: 15 - 26

Pg. 388: 1 - 12, 13,23,27

8-31

Graphing Sine and Cosine Functions
• Introduction to the Graphs of Sine and Cosine Functions
• Graphing Sine or Cosine Functions with different Coefficients
• Finding Maximum and Minimum Values and Zeros of Sine and Cosine
• Solving Word Problems Involving Sine or Cosine Functions

pg. 401: 1,5,7,11

9-5

Graphing Sine and Cosine Functions with Vertical and Horizontal Shifts
• Graphing Sine and Cosine Functions with Phase Shifts
• Fancy Graphing: Changes in Period, Amplitude, Vertical Shift, and Phase Shift

pg. 415: 1,5,7,9,21,23,25,27,33,35

9-7

Test 1

9-12

Graphing Other Trig Functions
• Graphing the Tangent, Secant, Cosecant, and Cotangent Functions
• Fancy Graphing: Tangent, Secant, Cosecant, and Cotangent
• Identifying a Trig Function from its Graph

pg. 426: 1,3,5,15,35

9-14

Inverse Trigonometric Functions
• An Introduction to Inverse Trig Functions
• Evaluating Inverse Trig Functions
• Solving an Equation Involving an Inverse Trig Function

pg. 437: 1,5,11,15,19,22,23

pg. 437: 27, 29, 31, 77

9-19

• Evaluating the Composition of a Trig Function and Its Inverse
• Applying Trigonometric Functions: Is he Speeding?

9-21

2: Trigonometric Identities
Basic Trigonometric Identities
• Fundamental Trig Identities
• Finding all Function Values (make sure this lecture is right!)

9-26

Simplifying Trig Expressions
• Simplifying a Trigonometric Expression Using Trigonometric Identities
• Simplifying Products of Binomials Involving Trigonometric Functions

pg. 459: 1,7,13,41

9-28

• Simplifying Trigonometric Expressions Involving Fractions
• Factoring Trigonometric Expressions
• Determining Whether a Trig Function is Odd, Even, or Neither

10-3

• Proving an Identity
• Proving an Identity: Other Examples

10-5

Test 2

10-10

Solving Trigonometric Equations
• Solving Trigonometric Equations
• Solving Trigonometric Equations by Factoring

pg. 494: 1,3,5,7,9,29,31,33

10-12

• Solving Trigonometric Equations Using the Quadratic Formula
• Solving Trigonometric Equations with Coefficients in the Argument
• Solving Word Problems Involving Trigonometric Equations

10-13

Mid term, last day to withdraw from a class without penalty.

10-17

The Sum and Difference Identities
• Identities for Sums and Differences of Angles
• Using Sum and Difference Identities
• Using Sum and Difference Identities to Simplify an Expression

pg. 468: 1,5,21 , 31, 35, 37

10-19

Double-Angle Identities
• Confirming a Double Angle Identity
• Using Double-Angle Identities
• Solving Word Problems Involving Multiple Angle Identities

pg. 477: 1,3,5

10-24

Other Advanced Identities
• Using a Cofunction Identity
• Using a Power-Reducing Identity
• Using Half-Angle Identities to Solve a Trig Equation

pg. 468: 9,11

10-26

3: Applications of Trigonometry
The Law of Sines
• The Law of Sines
• Solving a Triangle Given Two Sides and One Angle
• Solving a Triangle (SAS): Another Example
• The Law of Sines: an Application

pg. 513: 1,3,89,13,17,37,38,39,45

10-31

The Law of Cosines
• The Law of Cosines
• The Law of Cosines (SSS)
• The Law of Cosines (SAS): An Application
• Heron's Formula

pg. 522: 3,9,13,17,31,43

11-2

Test 3

11-7

Vector Basics
• An Introduction to Vectors
• Finding the Magnitude and Direction of a Vector
• Vector Addition and Scalar Multiplication

pg. 529: 1,3,7,11,13,23,31
pg. 539: 1,5,7,11,15,17,25,27,45

11-9

Components of Vectors and Unit Vectors
• Finding the Components of a Vector
• Finding a Unit Vector
• Solving Word problems Involving Velocity and/or Forces

11-14

Complex Numbers in Trig Form
• Graphing a Complex Number and Finding Its Absolute Value
• Expressing a Complex Number in Trigonometric or Polar Form

pg. 562: 1,3,13,15,17,23

11-14

• Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form

11-16

Powers and Roots of Complex Numbers
• Using DeMoivre's Theorem to Raise a Complex Number to a Power
• Roots of Complex Numbers

pg. 568: 1,5,9

11-21

• More Roots of Complex Numbers
• Roots of Unity

11-28

Polar Coordinates
• An Introduction to Polar Coordinates
• Converting Between Polar and Rectangular Coordinates

pg. 553: 1,3,7,11,13,15,45,51

11-29

Last Day to withdraw from a class

11-30

• Graphing Simple Polar Equations

12-5

Review

12-7

Final Exam

Item	Date	Discussion
3-100 point tests	Sept. 7, Oct. 5, and Nov. 2	No make up tests will be given. A missed test will be replaced by 1/2 of your final exam score. Note: Online students unable to take the tests in class, may take them in the physics lab BS 214 Wed, Thur, or Fri, of that week, 12 - 5 PM.
1-200 point Final Exam	Dec. 7	Final will be comprehensive.
Online homework- 200 points	Tuesday's homework is due at midnight the next night, Wednesday. Thursday's homework is due at midnight the following Monday.	Homework problems will given one point each, but your final score will be divided by the total possible and multiplied by 200. The Thinkwell website provides hints for most of the problems in case you get stuck. But there will also be online discussion sessions every Tuesday and Thursday evenings 6 - 8 pm. You may also obtain assistance via email.

Date	Topic / Thinkwell Assignments	B, Z, & B's hwk problems
8- 22	Angles and Radian Measure • Finding the Quadrant in Which an Angle Lies • Finding Coterminal Angles • Finding the Complement and Supplement of an Angle • Converting Between Degrees and Radians • Using the Arc Length Formula • Orientation to Math 113 Web page • Log onto Thinkwell and do first homework assignment • Log onto Blackboard and join a discussion session.	Pg. 364: 1,3,7,9,11,13,17,19,21,67, 69,73,75
8-24	Right Angle Trigonometry An Introduction to the Trigonometric Functions • Finding an Angle Given the Value of a Trigonometric Function • Using Trigonometric Functions to Find Unknown Sides of Right Triangles • Finding the Height of a Building	pg. 381: 5,9, 55,58
8-29	The Trigonometric Functions • Evaluating Trigonometric Functions for an Angle in the Coordinate Plane • Evaluating Trigonometric Functions Using the Reference Angle • Finding the Value of Trigonometric Functions Given Information About the Values of Other Trig Functions • Trigonometric Functions of Important Angles	pg. 381: 33,37,45,61,63 pg. 381: 15 - 26 Pg. 388: 1 - 12, 13,23,27
8-31	Graphing Sine and Cosine Functions • Introduction to the Graphs of Sine and Cosine Functions • Graphing Sine or Cosine Functions with different Coefficients • Finding Maximum and Minimum Values and Zeros of Sine and Cosine • Solving Word Problems Involving Sine or Cosine Functions	pg. 401: 1,5,7,11
9-5	Graphing Sine and Cosine Functions with Vertical and Horizontal Shifts • Graphing Sine and Cosine Functions with Phase Shifts • Fancy Graphing: Changes in Period, Amplitude, Vertical Shift, and Phase Shift	pg. 415: 1,5,7,9,21,23,25,27,33,35
9-7	Test 1
9-12	Graphing Other Trig Functions • Graphing the Tangent, Secant, Cosecant, and Cotangent Functions • Fancy Graphing: Tangent, Secant, Cosecant, and Cotangent • Identifying a Trig Function from its Graph	pg. 426: 1,3,5,15,35
9-14	Inverse Trigonometric Functions • An Introduction to Inverse Trig Functions • Evaluating Inverse Trig Functions • Solving an Equation Involving an Inverse Trig Function	pg. 437: 1,5,11,15,19,22,23 pg. 437: 27, 29, 31, 77
9-19	• Evaluating the Composition of a Trig Function and Its Inverse • Applying Trigonometric Functions: Is he Speeding?
9-21	2: Trigonometric Identities Basic Trigonometric Identities • Fundamental Trig Identities • Finding all Function Values (make sure this lecture is right!)
9-26	Simplifying Trig Expressions • Simplifying a Trigonometric Expression Using Trigonometric Identities • Simplifying Products of Binomials Involving Trigonometric Functions	pg. 459: 1,7,13,41
9-28	• Simplifying Trigonometric Expressions Involving Fractions • Factoring Trigonometric Expressions • Determining Whether a Trig Function is Odd, Even, or Neither
10-3	• Proving an Identity • Proving an Identity: Other Examples
10-5	Test 2
10-10	Solving Trigonometric Equations • Solving Trigonometric Equations • Solving Trigonometric Equations by Factoring	pg. 494: 1,3,5,7,9,29,31,33
10-12	• Solving Trigonometric Equations Using the Quadratic Formula • Solving Trigonometric Equations with Coefficients in the Argument • Solving Word Problems Involving Trigonometric Equations
10-13	Mid term, last day to withdraw from a class without penalty.
10-17	The Sum and Difference Identities • Identities for Sums and Differences of Angles • Using Sum and Difference Identities • Using Sum and Difference Identities to Simplify an Expression	pg. 468: 1,5,21 , 31, 35, 37
10-19	Double-Angle Identities • Confirming a Double Angle Identity • Using Double-Angle Identities • Solving Word Problems Involving Multiple Angle Identities	pg. 477: 1,3,5
10-24	Other Advanced Identities • Using a Cofunction Identity • Using a Power-Reducing Identity • Using Half-Angle Identities to Solve a Trig Equation	pg. 468: 9,11
10-26	3: Applications of Trigonometry The Law of Sines • The Law of Sines • Solving a Triangle Given Two Sides and One Angle • Solving a Triangle (SAS): Another Example • The Law of Sines: an Application	pg. 513: 1,3,89,13,17,37,38,39,45
10-31	The Law of Cosines • The Law of Cosines • The Law of Cosines (SSS) • The Law of Cosines (SAS): An Application • Heron's Formula	pg. 522: 3,9,13,17,31,43
11-2	Test 3
11-7	Vector Basics • An Introduction to Vectors • Finding the Magnitude and Direction of a Vector • Vector Addition and Scalar Multiplication	pg. 529: 1,3,7,11,13,23,31 pg. 539: 1,5,7,11,15,17,25,27,45
11-9	Components of Vectors and Unit Vectors • Finding the Components of a Vector • Finding a Unit Vector • Solving Word problems Involving Velocity and/or Forces
11-14	Complex Numbers in Trig Form • Graphing a Complex Number and Finding Its Absolute Value • Expressing a Complex Number in Trigonometric or Polar Form	pg. 562: 1,3,13,15,17,23
11-14	• Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form
11-16	Powers and Roots of Complex Numbers • Using DeMoivre's Theorem to Raise a Complex Number to a Power • Roots of Complex Numbers	pg. 568: 1,5,9
11-21	• More Roots of Complex Numbers • Roots of Unity
11-28	Polar Coordinates • An Introduction to Polar Coordinates • Converting Between Polar and Rectangular Coordinates	pg. 553: 1,3,7,11,13,15,45,51
11-29	Last Day to withdraw from a class
11-30	• Graphing Simple Polar Equations
12-5	Review
12-7	Final Exam