Online Video Lectures for Trigonometry MATH 1316

Online Video Lectures for Trigonometry MATH 1316, summer 2012

Daily Announcements:
Welcome to Trigonometry MATH 1316, summer 2012.
Go to The Start of Trigonometry Lectures then scroll down to the current lecture video.

Basic Information:
Access or timely update to this web site or MyMathLab is not guaranteed.
All information is subject to change. Attend all classes regularly and check this page as well.
NEW Course ID for MyMathLab/MML for summer 2012 is maesumi48385
TEST DATES: Tuesday July 24, Friday August 3, Wednesday August 15, subject to change
A basic scientific calculator is needed on tests.
Daily Time Requirement: 90 minutes class + a minimum of 4 hours of study.

Class format:
We will use what is called ``Now-U-Try, dialog-based, flipped, inverted, or upside-down format''.
This is described in Here1 , Here2 , Here3 , Here4 , Here5 , Here6 , Here7 , Here8 , Here9
In this method of teaching:
a) Students view the videos at home and take careful searchable lecture notes. (Mostly two lecture videos per day)
b) Students form study groups (2 or 3 students per group).
c) Students solve the homework problems and enter the problem/answers on their notebook and/or MML.
d) Students come to board during class time to solve homework problems.
e) Students get up to 10 bonus points based on their performance at the board and for the performance of the rest of their study group.
f) There may be a short quiz (1 point each) at the beginning of each class on the assigned video lectures.
g) So long as this format is used the tests will be open notebook.
h) If 2/3 of students vote for traditional class format then tests will be closed notebook.

Advantages of this teaching method:

You can replay the video to understand the lecture better.
You can review the video with a classmate or instructor.
You can pause the video, work a problem yourself, and compare with the presented solution.
You can view the video at your own place, time, and speed.
You get access to animation, graphing and useful links.
You get the most complete lecture notes. Now you cannot be absent.
Most importantly, by putting the lectures on-line, instructor's time in class will be freed for interaction with students. Errors can be corrected in real time, insights can be recognized, and hands-on instruction can become a reality. Class becomes a public tutoring place. If you have the stamina for it, that is the best approach. The instructor is not there to judge you at the board but he is there to push you to do your best. More like a coach than an examiner.

Extended Information:
0- Course information for summer 2012, as a PDF file

1- Text, access code, homework
You have the following two options.
(a) Use MML. (Buy a new text budled with software MyMathLab/MML or just MML access code for your homework.) Your MML homework score will be used as another test score.
(b) Do not use MML. The average of your two highest test scores will be counted as another test score.
Short version: Buy a new text bundled with MyMathLab (MML) ISBN 0-321-698630,
Use the course ID for the specific semester you are registering.
NEW Course ID for MML for summer 2012 is maesumi48385
Long version: If you have the time to maneuver the maze then read on:
Title: Trigonometry, second edition
Authors: Beecher, Penna, and Bittinger
Publisher: Pearson, Addison Wesley
about 250 pages, soft cover
This book is a third of College Algebra with Trigonometry by the same authors.
You may use MyMathLab (MML) software with this course.
The software checks homework, gives extra explanation, videos, graphics, etc.
ISBN for text with MyMathLab Access code is: 0-321-698630; This is available in university or KampusKorner bookstores.
Once you have a new access code you go online to register your access code for one course.
Use the course ID to get access to my trig course :
You can start doing the homework as soon as you register. The homework list shows up after you register online.
ISBN-10 for text alone (without MML) : 0-321-53630-4;
ISBN-13 for text alone (without MML) : 978-0-321-53630-3;
MyMathLab access code alone is also available in bookstores and online (ISBN ??).
If you buy pre-owned access code you want to make sure that it is not registered. That is, an access code that somebody purchased but never used to register for any course (as might happen in other sections of 1316 since they do not use MML!).
You get access to the ebook for the course (as well as the college algebra component of the original book) through the access code.
So, in summary, you have several choices depending on your decision about used/new and with/without access code.
If money is no object (!) you will buy a new book bundled with an access code.
Else, if you are on a budget, then either buy MML or a used book (but not just an ebook by itself)
If you feel comfortable reading an ebook on a monitor then just buy the MML access code. That, by itself, is sufficient since it gives access to ebook as well.
If you buy a used text you have to check if it comes with an un-registered access code. If it doesn't then you have the option of buying an access code.
If you feel confident about your trig ability and think you can do well enough without MML, and it is enough for you to check the answer to odd-numbered problems then just buy a used text.
Phew! If this is not clear ask!

Bad idea: Buying a time-limited Ebook by itself. For our course it usually does not make sense to just buy an ebook. Unless that is exactly what you want, for some particular reason. It is better to buy MyMathLab which contains the ebook.

Questionable idea: Waiting until late in the semester, checking your grade, deciding to do the online homework in the last few weeks, buying MML then, asking me to change the deadlines, saying that you will do 500 homework problems in 2 weeks!

Let the buyer beware: The new styles of selling a text can be confusing. Do your research before you pay. For example some digital texts are not for download, just for viewing, and have limited life (eg. the "life of the edition" which is usually 3 or 4 years from copyright year. This means if you buy the book just before its upgrade time or in the last semester it is supported by the publisher and fail the course then you may need to buy the new version in the next semester. However the publisher may grant an extension, so keep your receipt. In case you rent the text then your rental agreement specifies 180 days or 360 days etc). For our text the "life of edition" is unclear and apparently has been extended, so we do not know when its end of life will come! However the publisher may grant an extension to students whose texts expire. Also, note that MML can only be registered only once. Ebooks and MML probably cannot be returned.

2- Tests:
There will be 3 tests Tuesday July 24, Friday August 3, Wednesday August 15, subject to change. These dates are subject to change. They will be sectional (not cumulative, eventhough basic ideas show throughout).
Review problems done in class, videos, sample problems done in text, and homework assignments. Do read the text itself.

3- Prerequisites
You DO need a working knowledge of College Algebra.
Did I emphasize that you need a WORKING knowledge, not an AS-IS knowledge?
Just having taken College Algebra some time in the past won't do. It must be at your fingertips. This is very important and without familiarity with algebra the course becomes quite hard to follow. In particular you need to know about functions, graphing, and inverse functions. There are many places you can go for a review. Here are some choices :
3a. WTAMU Algebra Review .
3b. Hoffmann Algebra Review.
3c. Your MyMathLab Access Code also provides you with an ebook containing an Algebra text alongside with your trig text.
3d. University of Idaho. Review Part A
3e. There are a few video lectures below which can be of help.

4- Online courses on trigonometry
Best way to study for a course is to pre-study.
4a. University of Idaho. Review Part B
4b. D. E. Joyce Trig Course (interactive text)

5- Who should take a course in trigonometry?
Students of quantitative sciences (computer, physics, chemistry,...), Engineering, Mathematics, Teacher education.
If you are from other disciplines or planning to change your major you are still graded based on the same standards as all other students.

6- Is this course suitable as a general purpose math requirement?
It depends. Nowadays my typical answer is NO.
I teach the course for the audience who actually needs it, and not as a repeat of an introductory high school course.
Trig is very meaningful and fun, but only to a person who has the prerequisites for it.
Trig is laden with a very large number of similar sounding formulas. Learning that stuff takes many many many hours.
The fun starts AFTER you learn all that stuff. Unfortunately most student do not spend the time it takes to learn trig.
Taking this course just because it fits your time schedule and you "can be done with 3 hours of required math" is a good bet on losing $$$ and more.

7- What is a good, easy, meaningful math course?
A course on Introductory Statistics is your best bet, if you want something with minimal prerequisites and the most general relevance. Check with your degree plan to see if it is acceptable for you. There are several choices available.

8- Is trigonometry useful?
Yes. Trigonometry is the art/science of measuring triangles. It couyld be for plain measurement or for advanced applications such as explaining where the rainbows come from or for designing quality lenses. In some applications, trigonometry is the art of measuring things you cannot reach. Many types of "inaccessible" measurements rely on using trigonometry. Large scale items, as in tall buildings or mountains, or very small items, as in molecules, can be analyzed using trig. There are many applications in MATH 2413 calculus 1, a lot of formulas in MATH 2414 calculus 2, meaningful application in MATH 2415 calculus 3, as well as in MATH 2318 linear algebra and MATH 3301 differential equations. Then you see a lot of these in circuit analysis and heat transfer or Fourier series. The formulas we learn in 1316 are scattered through out different areas of math, science, and engineering. Land surveyors and cartographers dream in trigonometric HD.

9- For the philosophical/historian in you :
A readable introduction to the role of trigonometry in human history. If you object to memorizing all these formulas, you want to put your mind were your mouth is, and you want to know something significant here you go
Trigonometric Delights by Eli Maor

10- Extra points, OCE
You get 5 points added to your lowest score for completing. The Online Course Evaluation
Get a print out of the page that shows you completed the evaluation for this course.
Write your full name on it.
Give the hard copy to me by the final.
Make sure you do NOT print your private answers! just the page where it says you are done.
Also remember your MML homework score can improve your grade.

11- General tips on home work:
a- Do what you can. At least do one problem from each type. If you have difficulty with a problem repeat with similar type problems until your speed improves and the solution steps become almost automatic for you.
b- Follow the methods used in class or shown in the text book.
c- Compare your final answer with the solution to the odd-numbered problems at the end of the text or on MyMathLab.
d- Form study groups.
e- Use free tutoring available in L209. Talk to several tutors. Ask questions collectively.
f- Bring up your un-answered questions in office hours.
g- Bring up your un-answered questions in class.

12- How to help yourself get ready for tests:
(a)Give yourself self-tests:
(a1) Write problems, whose solutions you have seen, on a flash card.
(a2) Indicate where solution can be found and allocated time. Store in a box.
(a3) Draw 10-20 random questions, give yourself a timed test (time=sum of indicated times on flash cards).
(a4) Grade using the available solutions.
(a5) Re-study problems you missed.
(b) Make sure your your lecture note/home work note-book is complete, searchable, and readable to yourself. You should be able to find the solution of a worked-out homework problems with ease (otherwise you cannot give yourself a self test effectively). You may want to number your pages for the indexing to work with ease.
(c) The only digital device you are allowed to have in class is a BASIC scientific calculator. Devices capable of wireless communation, text/photo storage etc are not allowed.

13- Calculator Policy: Only BASIC scientific calculators are allowed. These calculators cost about 10-30 dollars, and do NOT have the following capabilities: Graphing, programming, text storage, wireless connection, symbolic equation solving, differentiating, or integrating. Advanced or graphing calculators (such as TI 80 etc) and ipod/cell phone calculators are NOT allowed on tests. If in doubt ask before opening the box.
If you do not have the proper calculator then you will take your test without one. Use of forbidden electronics will result in 50 penalty points.
You do need to practice using the calculator EARLY ON and become confident about its operations. Do keep its manual and find the website of the calculator for future reference. The calculators with multi-line mathematical style display can show your steps and reduce data entry error. Casio FX-115ES and Sharp EL-W516 are two calculators below $20 with this ability.
Casio FX-115ES Manual This is easier to search than the printed one.
Casio FX-115ES Appendix Most of the words/buttons here are actually images and therefore not searchable.
Sharp EL-W516 Manual
Remember the text in PDF files is searchable. Look for the binocular icon or press CTRL f.

14- Advanced Online Interactive Calculators with Graphics:
Wolfram Natural Language Calculator .
Function Analyzer.
InstaCalc, a calculator with spread sheet concept .
Calc98 a downloadable basic calculator.
Power Calculator Downloadable calculator from MicroSoft. Look under Power Toys tab.

15- Solution Manual Policy: Students are not to bring solution manuals to class. Copying solutions to homework problems from any source is not allowed. Students should understand their solutions and be able to reproduce it from scratch. Copying final answer from the book, at the end of an incorrect solution, is bad style.

16- A short review of some basic algebra concepts
See Item 3 above for more extended resources.
(a) Exponential Functions. Definition of exponential function. Extension to negative, zero, rational, and irrational exponents Properties of graphs of exponential functions. Base e exponential functions. Applications to simple population problems. Doubling time. Applications to radioactive problems. Half life.
Extras:
applet shows y=a^x becomes tangent to y=x+1 when a=e.

(b) Introduction to Functions. Simple description of functions, domain, range, arithmetic operations, composition, decomposition, substitution.
Extras:
Here you can test your knowledge of basic functions (linear and quadratic) by this association game.
Here you can experiment with a JAVA applet showing arithmetic operations on functions (addition, subtraction, multiplication, division, as well as inverse functions and composition). Choose two functions from the drop down menu, or type them yourself. For example you can type 5*x^3+20*cos(pi*x)+e^(-2*x). Notice that we use ^ for power, * for multiplication, pi for pi=3.1415926535897932..., and e for e=2.718281828459045... . Set boundaries for the picture by modifying xmin, xmax, ymain, ymax, and choose which activities you wish to graph. Try to guess what the graph is going to look like first and then verify it.

(c) A Quick Preview of Trigonometry Angles, vertex, ray, opening, initial side, terminal side, positive or counter-clockwise direction, negative or clockwise direction, winding number, standard position, quadrants, circumference of a circle, measuring angles, degrees, radian, grad, circle, cycle, rotation, round, length of an arc, area of a sector, six trig functions in terms of adjacent, opposite, and hypotenuse, solving a right triangle, six trig functions for arbitrary angles, trig identities: Pythagorean, ratio, negative, sum of angles.

Extras:
the six trig functions in a unit circle setting.

the animated drawing of sine, cosine and tangent in a JAVA applet. click on the third big red box titled: Applet: the graph of sin, cos, and tan.

the ordinary graph of sin, cos, tan, arcsin, arccos, arctan. Click on "Graphs of elementary trigonometric functions".

(d) Inverse Functions Simple description of inverse functions. Domain, range, graph, slope, existence, horizontal line test.
Correction: there is a typo around minute 8:50 where I write y goes to (y-2)/3. the correct form is y goes to (y-3)/2.

(e) Logarithmic Functions, inverse of exponential functions Simple description logarithms, rules of logarithms, base 10 and base e, graphs.

(f) Quick Preview of Inverse Trig Functions. arcsin, arccos, arctan, graphs, and special values. Review from pre-calculus.

(g) Review of Problems on Inverse Trig Functions. Review of sample problems.

Lectures on Trigonometry

Read Section 1.1 Pages 2-5
Lecture 1: The Six Trig Functions

Read Section 1.1,
Lecture 2: reciprocal identities, cofunction identities, famous angles (30,45,60 degrees)

Read 1.2, Applications
Lecture 3: degrees, minutes, seconds, calculating inverse trig functions, applications: height of a mountain

Read 1.3
Lecture 4: regular polygon problem (1.2, 29), arbitrary angles,

Read 1.3
Lecture 5: trig functions of arbitrary angles, given angles or coordinates

Read 1.3
Lecture 6: trig functions of arbitrary angles, given equation of terminal line, reference angle, sign of trig functions

Read 1.4
Lecture 7: Cicle as a Number Line, Radians, Arc Length

Read 1.4
Lecture 8: Radians, Arc Length, angular speed

Pre-Read 1.5 and review graphing concepts from college algebra: point plotting, x and y-intercepts, symmetry, asymptotes, domain, range, etc. Use the following apps for 1.5 and 1.6.
the six trig functions in a unit circle setting.

the animated drawing of sine, cosine and tangent in a JAVA applet. click on the third big red box titled: "Applet: the graph of sin, cos, and tan".

the ordinary graph of sin, cos, tan, arcsin, arccos, arctan. Click on "Graphs of elementary trigonometric functions".

Wolfram Natural Language Calculator .
Function Analyzer. You can use this for graphing and root finding.
(This also has many advanced features such as differentiating, integrating, and Taylor series which you may use in a calculus course. Fractional powers of negative numbers should be handled carefully here.)
Multiple Function Graph Explorer 1.
Multiple Function Graph Explorer 2.
InstaCalc a calculator with spread sheet concept .
Calc98 a downloadable basic calculator.
Power Calculator a downloadable calculator from Microsoft with graphics.

Read 1.5
Lecture 9: A brief review of graphing concepts from college algebra: point plotting, x and y-intercepts, symmetry, asymptotes, domain, range, etc

Read 1.5
Lecture 10: Graph of Sine and Cosine

Read 1.5
Lecture 11: Graph of Sine, Cosine, and Tangent using unit circle,

Read 1.5
Lecture 12: Graph of Cosecant, Secant, and Cotangent using reciprocal identities, graph of Cotangent using the unit circle,

Read 1.5
Lecture 13: Negative angle and Reflection Identities, Sin(-x), Sin(Pi-x), Sin(Pi+x), etc

Read 1.6
Lecture 14: Graph of transformed Sine and Cosine functions: a*Sin(b*x+c)+d

Applet showing Transformations of Sine and Cosine Note format is a*Sin(b(x-pi h))+k, so the phase shift is (pi*h)

Read 1.6
Lecture 15: Graph of transformed Sine and Cosine functions: a*Sin(b*x+c)+d

Read 1.6
Lecture 16: Examples for Graph of transformed Sine and Cosine functions: a*Sin(b*x+c)+d

Read section 2.1 Pages 102-107
Lecture 17: Identities (Pythagorean)

Read section 2.1 Pages 102-107
Lecture 18: Identities (reciprocal, negative angle, examples)

Read section 2.1 Pages 111
Lecture 19: Examples for Transformations and Lecture on Identities (cosine of sum and difference)