Each class will begin with whatever announcements need to be made, and then I'll cut you loose to work on your homework and test preps.

If you want me to cover a particular concept/example/exercise during the face-to-face, hit me up in E-Mail (Use Classlist on D2L), and I can prep specifically for your question or even make an extra video ahead of time, in some cases.

• 10/6 Notes
• 10/6 Video
  • I gave a very uninspired speech covering angle-sum, double-angle, and half-angle questions, from old midterm and from WebAssign homework. I built a cosine function from info about its high point, and low point.

    We talked about the Midterm: Monday, October 13th OR Tuesday, October 14th, Horizon Hall (HOR) 107. Bring ID, scientific calculator and pen or pencil.

    Show up any time any of those days, between 8 am and 6 pm to take your midterm.

    You are permitted a one-page (both sides) cheat sheet with whatever formulas you want on it. I recommend AGAINST putting examples of particular exercises on there. Students who do that rarely seem to succeed on tests. You want to know how to work all the type problems, and your cheat sheet should just be the identities and formulas.

• 10/1 Notes
• 10/1 Video
  • We didn't have (m)any questions, so I dove into Section 2.3 (due in one week), and showed basic trig-equation-solving techniques.
• 9/29 Notes
• 9/29 Video - 1 - Worked Examples. List of identities.
• 9/29 Video -2 - Worked my version of 2.1 Part II #1. We learn to factor to find zeros. We can also use zeros to help us factor. This is my "sledgehammer" for factoring quadratic polynomials.
  • We discussed identities from Sections 2.1 and 2.2. I briefly demonstrated the Sledgehammer Method for factoring, when in doubt: Just use quadratic formula to find the zeros and then use the zeros to reverse- engineer a plausible factorization.
• 9/24 Notes
• 9/24 Computer Algebra graphs
• 9/24 Video 1 - Inverse trig graphs from trig graphs.
• 9/24 Video 2 - sin(arctan(7/24))
• 9/24 Video 3 - 1.6 #28 is a graphing utility question. I did some hand-sketch stuff, but this is a tech question.
  • We did some "How to graph inverses." Then I anwered a question about 1.7 #24.

    I shared a link to a cheat sheet.

    We talked about my 5 triangles vs the 12-point unit circle.

• 9/22 Notes
• 9/22 Video 1 - Quick intro to Inverse Functions.
• 9/22 Video 2 - A more advanced question from Section 1.8
  • Things seem to be going very well. I still owe you guys a working grade report. I've fixed the issues but I need to send the new reports to you. As I can barely type, today, I think I'm just going to put my wrist on ice. Might not be 'til tomorrow...
• 9/17 Notes
• 9/17 Video
  • Today, we discussed the basic graphs of sine, cosine, tangent, and cosecant. Basic graphs for secant and cotangent are obtained from graphs of cosine and tangent, respectively, in much the same manner as tangent and cosecant were obtained from graphs of sine and cosine.

    I had a question from Dany that I didn't catch. Sorry I lost you, today, Dany! I was just too keen on covering the graphing. If you already did your 1.5, then you probably already saw everything I said, today, in the homework notes and videos, which give pretty comprehensive coverage of all the skills.

    In direct response to your comment, yes. I encourage you to use graphing utilities to help you visualize these functions, especially the cosecant, secant and cotangent. At the same time, I want you to be able to do as much as you can with just your brain, pencil, and paper. Next Monday, I will try to show how to get graphs of cosecant, secant, and cotangent from the graphs of sine, cosine, and tangent, respectively.

    I think you were 1 lecture ahead, and I didn't honor it very well. I could easily have demonstrated using DESMOS and/or WOLFRAMALPHA, for quick "intuition-building" visuals. These tech tools can also be a quick check on what you are attempting to master with paper-and-pencil. But eventually, we want you to do as much as possible by hand, with the assistance of a scientific (not graphing) calculator.

    To know the limits of what might be asked, please refer to Old Midterms and Finals .

    So I want you to thoroughly understand the graphs of sine, cosine, and tangent. The rest can be reasoned out, with the more classic, paper-and-pencil techniques I will stress. It's paper-and-pencil that will be tested on the Midterm and Final, and the paper-and-pencil skills are what you need down the road, if you want to know how to tell a computer to do the work. I caution against being too technology-dependent.

    When you're too tech-dependent, you may make incorrect reports because you hit one wrong key, but didn't have the commen sense to realize that your results were ridiculous. "Really? 10 tons of flour to double my cake recipe that calls for 4 cups?"

    There's a wealth of material from College Algebra on graphing basic functions and transforming them into more complicated functions' graphs. Check out Section 1.5 Homework Notes and Videos.

• 9/15 Notes
• 9/15 Video
  • I mentioned the need to get you a new Grade Report, because of a flaw in the formula for "without quizzes." I showed how the grade with and without quizzes is calculated. I originally said the Quiz grade would be rolled into the Written-Test grade, making it weigh 50% of your overall grade, which is actually a good way of breaking things down, as the written, proctored test, shows exactly what you're capable of under a time control.

    Instead, what I do is spread that 15% proportionally across all categories and average over 85 instead of 100, with the remaining categories remaining the same, relative to one another, just without the Quiz category being included.

    Today, we talked about some 1.4 questions from WebAssign. 1.4 is when I get out of jail and can show you the main skills, without holding anything back. In the past, I've skipped 1.2, to keep you from trying to memorize the 12-point unit circle, when you only need 3 triangles, 2 degenerate triangles, and logic, to find any of the 12 points of interest around the unit circle. Less memory. More ideas.

• 9/10 Notes
• 9/10 Video
  • We talked about the standard triangles (2) you need to draw for sin(t) = 2/3, the two (2) triangles for the equation sin(t) = - 2/3, and the same for cosine and tangent. If you're faced with a secant, cosecant or cotangent, just flip the fraction upside-down and use what you know about sine, cosine, and tangent!

    We discussed trig functions of any angle, which is Section 1.4. The same ideas that we learned for Quadrant I apply to the other 3 quadrants, except you have to keep straight which (if any) of the x or y are negative.

• 9/8 Notes
• 9/8 Video
  • We covered an array of topics, mostly from Section 1.3, pertaining to Week 2 Written Assignment.

    About all I really use the Unit Circle for is to prove the Pythagorean Identities that are used on the later exercises for 1.3 and the Week 2 Written Assignment.

    Remember, you're free to call me, any time, at 970-290-0550.

• 9/3 Notes
• 9/3 Video
• 9/3 Video 2 - Jordan asked a good question.
  • Today, I showed the 5 triangles that, with some understanding, can replace the entire 12-point unit circle BS.

    This isn't for everyone, necessarily, but it will really speed things up and help your visual understanding, compared to memorizing sine and cosine for 12 angles, separately! (36 items versus (really) 3 triangles and your reasoning skills.)

    I did NOT show how you'd solve sin(t) = 1/2 in detail. I will next time, so you see that basic trig-equation-solving technique as early as possible, whether it sinks in, or not. If it does sink in, this class will be a snap for you! If it doesn't sink in, right away, you'll just pick it up the next time or the time after. When I learned this stuff, I usually failed at each new thing 2 or 3 or 10 times before it clicked.

    I was never all that smart. I just persevered until I got it, even if it took me all night. "You figured that out, fast!"

    "Nah. I just stayed up all night. I've spent 12 hours on this since last we spoke."

    I showed something of how the website is structured. Bare bones. Basic. Best practices for the 1980s, built to minimize "mean time before finding" (MTBF).

    Jordan asked me about 1.1 #24 part (b), and I did a poor job of it, but we arrived at the correct answer by dividing our answer for Part (a) by 3600 (seconds per hour) and multiplying by n. The second part of Part (b), we just replaced 'n' by 't,' as the rate was 1 revolution per second on the front sprocket.

    I'm still not happy with my explanation, but on the bright side, I'll only ask you questions on Part (a). It finally clicked in my brain after Jordan had the answer (and quite enough of me!). I'll take a stab at it on Monday, if I remember and/or anyone asks.

• 8/27 Notes
• 8/27 Video 1 - We discussed the definition of the radian and its relationship to arc length, angular speed, and linear speed (spinning pulleys, saw blades, bicycle wheels, ...)
• 8/27 Video 2 - Excellent question(s) about how to write-up the Weekly Written Assignments. This gave me the bright idea of sharing the Solutions to the Week 1 Written Assignment.
  • We discussed arc length as it relates to radian measure, and related these to linear speed. The second video was my explanation of the general way to attack the material, where the on-demand homework help is, and - IMPORTANT - explained what the expectations are for "context" of the Weekly Written Work. I also did something I should never do: I supplied the Solutions to the Week 1 Written Assignment?! That'll give you all a better idea of how I hope and expect Written Work to be done.
• 8/25 Notes
• 8/25 Video
  • We had a half-decent informal orientation for everyone on the first day of class!