Analytic Trigonometry Math 144 Syllabus Spring 2007

2 semester credits

For section

Math 144 Analytic Trigonometry Section 003 WF 2:40 - 3:30 PM MG 118

Instructor

Tom Conklin

Email: twconklin@cableone.net

Office: MG 214D

Office Hours: WF 12:30 - 2:30 PM

W 4:30 - 7:00 PM

Class Website http://math .boisestate.edu/~tconklin/Math 144. html

Become familiar with the class website. It will have notes, worked out problems, calculator help and lots of supplemental material to aid in your learning.

BSU Catalog Descriptions

MATH 144 ANALYTIC TRIGONOMETRY (2-0-2). Right-triangle and circular-function approaches to trigonometry. Trigonometric Identities. Graphs of trigonometric functions; amplitude, frequency, phase shift. Inverse trigonometric functions and their graphs. Polar coordinates, polar representation of complex numbers. Credit cannot be granted for both

MATH 144 and MATH 147. PREREQ: MATH 143 or satisfactory placement score.

Prerequisites

MATH 143, with a grade of ``C'' or better; or sufficient score on COMPASS placement exam; or a 93<sup>rd</sup> -percentile score on the ACT or SAT. The rationale for these prerequisite is to ensure that students have an adequate level of ``mathematical maturity'' as well as specific background knowledge.

Jurisdiction

This course is controlled by a departmental committee, whose members may or may not be teaching the course. All sections use the same text, which is chosen by the committee. The committee also writes a syllabus detailing which sections should be covered and how much time should be allotted to each. Exams, homework, and grading system are left to the instructor.

Objectives

The objectives of MATH 144 reflect all four of the Department's teaching goals:

Appreciation of mathematical patterns:

MATH 144 presents several mathematical patterns:

• elementary proof patterns;
• an almost-axiomatic pattern of trigonometry;
• elementary duality patterns such as function inverses and the great geometry-algebra pattern;
• elaboration of the Pythagorean pattern to circular trigonometry.

Awareness of applications:

MATH 144 presents the following applications while laying groundwork for study of further applications in subsequent courses:

• compound interest and exponential growth and decay;
• trigonometric applications such as surveying and circular or oscillatory motion;

Mastery of some mathematical tools:

geometric effects of algebraic transformations;

algebraic effects of geometric transformations;

algebraic address of exponential and trigonometric phenomena;

use of ``appropriate technology'' to investigate problems.

Mathematics as a language:

algebraic language and its geometric consequences;

geometric language and its algebraic consequences;

grammar of communication with computers and calculators.

MATH 144 relates to the General Learning Outcomes of the University Core-Curriculum Philosophy as follows:

Critical Thinking/Problem-Solving Skills

• This course promotes critical thinking and problem-solving skills on a very narrow class of abstract problems. It is not a  problems'' course: for each mathematical topic covered, the course presents an array of problems which can be addressed successfully using the insights and techniques appropriate to the topic.

• Periodically, the students must have some problems presented free of any particular context, in hopes that they break down the ``topic-to-problem'' structure of the course's presentation to arrive at a successful ``problem-to-topic'' solution.

Communication Skills

• An ongoing battle is to encourage the student to document problem solutions with appropriate prose, mnemonic variable names and labeled diagrams.

• This eventually aids the student in communicating problem descriptions and solutions to others as well as in communicating about problems with the student's own self.

• Student who have attained these communication skills and habits exhibit the ability to solve non-routine problems, problems not immediately transparent, problems whose solution may require time spent several different days.

Cultural Perspective

Persons lacking the minimal algebra and geometry perspectives of MATH 144 are at a disadvantage if life ever requires coping with scientific exposition or argument. That is, such persons are walled off from any appreciation of the basis of the scientific part of our culture.

Breadth of Knowledge and Intellectual Perspective

MATH 144 aims to promote a sensitivity toward numeric inputs and quantitative relationships in general. Thus, MATH 144 aims to promote a sensitivity toward numeric inputs and quantitative relationships in general. Thus, MATH 144 at the launch point of an acculturation effort which can lead to membership in the western scientific-technical subculture. Upon completion of this course, students should:

1. Be able to use the concepts of function, relation, and graphs.
2. Be able to use the algebraic and geometric language of mathematics correctly and effectively.
3. Have skill with manipulative algebra and the basic properties of elementary polynomial, rational, and transcendental functions.
4. Particular trigonometric knowledge and skills:
1. a working knowledge of right-triangle trigonometry and the trigonometric functions in this setting: sin, cos, tan, arcsin, arccos, and arctan.
2. a working knowledge of the unit-circle
3. circle geometry: tangent lines, arc length, radian measure.
4. trigonometry and the circular functions in this setting: sin, cos, tan, arcsin, arccos, and arctan. This includes the famous ``by-heart'' values of the functions: at 30 , 45 , 60 , 90 , 120 , 315 , 540 and their radian-measure versions.
5. a working knowledge of trigonometric graphs: sinusoids, tan, sec, and the inverse-trigonometric graphs.
6. a working knowledge of the basic identities: the Pythagorean identities, the sum formulas and the multiple-angle formulas.
7. skill at writing proofs of trigonometric or logarithmic identities.
8. skill at solving trigonometric equations and the use of graphs or symmetry to find all their solutions.
9. Have skill in translating problems to relevant prose, graphical, diagrammatic, or algebraic form.
5. Exhibit a working understanding of reflection, symmetry, and translation of graphs.
6. Be able to solve ``routine'' problems efficiently and have at-least-occasional success with more challenging problems.
7. Be able to cope with the problems inherent in solving equations for polynomials with degree greater than 2 and elementary transcendental equations.
8. Be able to avoid calculator-generated gaffes. Although MATH 144 does not teach calculator or computer skills as an alternative to algebraic techniques, it does bear some responsibility to study use of powerful graphing and algebraic calculators and attendant pitfalls.

Assessment of Learning Objectives

These objectives are periodically assessed via input from client departments and from instructors in MATH 144 and subsequent courses. Although the objectives have not changed in many years, their realization has changed over the time in response to learning research and technological progress.

Assessment of Student Progress

Students will be assessed by evaluating their ability to do problems based on the learning objectives. The problems will occur in several contexts:

Constant and frequent homework serves as both as a learning and an assessment tool.

Routine classroom student assessment can be based upon discussion contributions and contributions to group activities. In-class exams are designed to give students the opportunity to demonstrate their ability to work mostly-routine problems.

Topics and Approximate Timeline

The TENATIVE schedule for the term can be found on the website. While it will not be adhered to rigidly, it should give you an idea of how we will progress through the material.

Text

As of Spring, 2007, Precalculus, 5th edition, Stewart (Brooks/Cole).

Policies

Use of Calculators

Calculator use is encouraged, but the student must be able to use fundamental concepts to solve problems.

Format, Student Activities, and Grades

Class meetings involve a combination of lecture, questions and discussion, and sometimes small group activity; the instructor chooses the appropriate mix.

Homework (assigned problem sets) is an important part of the course, but consists mainly of routine problems. Evaluation will be comprised of performance on exams, quizzes, and assigned problem sets. The instructor chooses the exact grading scheme, but a typical distribution (this is an example) of points might be:

Example:

Problem Sets (4 @ 50 points each) 200

Regular Exams (4 @ 100 points each) 400

Total 600

Letter grades are usually based on a standard scale like below (with the instructor having the discretion to lower these cut-offs if warranted).

A 90% of total possible points or more 540   600 points

B 80% to 89% of total possible points 480   539 points

C 70% to 79% of total possible points 420   479 points

D 60% to 69% of total possible points 360   419 points

F Less than 60% of total possible points 0   359 points

Attendance: Experience shows there is a direct correlation between attendance and grades. This class is being held for YOUR benefit, you are expected to attend.

Cell Phones and Pagers: Students should have cell phones and pages switched off as a courtesy to the rest of the class and instructor.

Make-up Exams: Exams, Problem Sets and Quizzes can be made up only if the absence is excused (plausible valid reason AND known beforehand). Contact me (phone, email, etc.) before the absence. The exam or quiz should be made up as quickly as possible following the absence via arrangements with me.

Final Exam: Monday 5/7/07 3:30 PM Math 144 section 003

Student Code of Conduct: Students are expected to know and adhere to the policies in the Student Code of Conduct, found at http://www2.boisestate.edu/studentconduct

To the Student:

One of the best ways to learn anything is to explain it to someone else. Working in groups is a good way to provide yourself with this opportunity. Get to know others in the class and try to get together and work problems.

Math is not a spectator sport. You will need to actively participate, roll up your sleeves and get that pencil moving. You will also need to move your brain. Expect to have to think about concepts and problems. Some of the problems you will encounter will teach you new techniques: like playing scales in a musical instrument, or running laps around a track. You might not see the point immediately, but they are strengthening you so everything will come together when it counts. Think of them as push-ups for the brain and practice them often. Some problems will require you to think hard and pull concepts together (at this point you will be glad you did your push-ups). Take some time with them, talk about them, take breaks if you are getting frustrated, ask for help if you are stuck, enjoy the process: you are learning.

Thinking and understanding concepts will be emphasized here. To paraphrase Albert Einstein,  The only thing you absolutely must know is the location of the library.  In your situation this means you will probably always be able to find the formula you need somewhere. However, you will need to be able to set up your problems so that you know exactly what it is that you need! Since you will probably take about six more courses (depending upon your major) which utilize the concepts from this course, it will be especially important to understand what is useful or applicable in a particular

context. This is why understanding the process for solving a particular type of problem is emphasized over memorizing formulas. In most cases, if you understand the concepts, memorizing a formula becomes completely unnecessary because you construct the necessary tools when needed.

Some Concrete Pointers:

Classes are held for your benefit. If attending class wasn't important, all college courses would be by correspondence, and your tuition would be much lower! During class your instructor will go over examples, which are important, and most likely not in the book. It often helps to have a new concept explained in several different ways; the book and the lecture

are two different ways which are readily available. Information about quizzes, exams, and due dates is often given out in class. This will help you pace your studying. Math courses are sequential, so the stuff you see on page 191, for example, will enable you to make sense of a lot of the stuff you will see on page 192. As one instructor was heard to say,  Everything you have learned since you were three can be used in this class.  Hence you will not be helping yourself if you  cram  right before an exam and forget the material immediately afterward. As instructors, we note a definite correlation between grades and class attendance. What's the point? GO TO CLASS!

Learn to read math. The plethora of information to be found in your textbook is astounding. However, math books are not meant to be read like novels (even though they are often exciting and dramatic). It is generally best to read the sections of the book to be covered in lecture through quickly to get some idea of what is there before going to lecture. After the lecture read through it carefully, with pencil and paper in hand, working through examples in detail and taking notes. Make a list of questions to ask at the next lecture. One thing to bear in mind while reading your text is that the result of an example is often secondary to the process used in obtaining the result. This is one reason you should be sure you understand all the details the author left out (most likely intentionally). Also, many techniques for solving problems are displayed elsewhere than in examples, so read all of the text of the appropriate section. Even though it sometimes may not seem to be the case, the text does give the tools to do the homework problems.

Just as you must play a lot of basketball (or chess) to be good at it, you must DO a lot of math in order to be successful. At minimum, work every problem your instructor suggests. If you are having trouble or want more practice, work other problems in that section or get another book and work problems out of it. Most texts also have ``additional'' or review problems at the end of each chapter. These may or may not be arranged by section. If you are having trouble getting a correct answer to a problem, think about what is going wrong, that way you can learn something new and prevent yourself from making the same error in the future. Don't settle for a correct answer that you don't understand.

Work problems more than once: a good way to start off a study session is to start by working some problems from the last few assignments. Work problems until you can do them quickly and they become your friends. You can even name the most difficult ones. When reviewing or re-doing a problem, thing about why you take the steps you do, rather than simply repeating the problem in a robot-like fashion. Remember, the process is usually more important than the result.

The fastest way to get into trouble in math is to not do the homework. Remember, similar problems will probably show up on quizzes and exams, where you will be expected to work them quickly and accurately, probably without the book in front of you. Also remember that you will get more out of your homework time if you minimize distractions, i.e., turn the TV or stereo off.

Contrary to many students' opinions, your instructor wants you to succeed. Extremely rare is the instructor who will intentionally put completely different material on an exam that what was covered in class. For this reason, pay attention to your instructor. Then READ the class notes and be sure you understand them, filling in any missing details. Use your notes as well as the text when doing homework. Review your notes regularly and pay attention to the comments your instructor writes on your work. Read carefully all supplemental material provided by your instructor. Remember that if your instructor thinks an example is important enough to do in class, or takes the time to prepare a handout, it may also be of sufficient importance to test you on it.

Quizzes and exams can be the bane of your existence, or they can be showcases of your mastery of the material. When studying for them, work every homework problem assigned in the sections to be covered (more than once!), paying special attention to why you take the steps you do, and why it works. Review and work through examples in your notes and the text, again with particular emphasis on the process being used. Each section of your text has a central idea or concept. In many cases, this central idea depends in some way on an elementary concept with which you are already familiar. For example, finding volumes of some solids is simply an extension of finding areas of some geometric shapes that you already know. If you are able to explain exactly what the  nugget  of a section is and on what basic  stuff  it depends, chances are you are well on your way to a good understanding of the material at hand. This is  distilling  the material. You should regularly  revise  your  macro view  of the material covered and  speculate  where it might be leading.  Linkages  between ideas that are very important!