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.

• 1/20 Notes
  • LOL! I actually called a meeting on MLK, Jr. holiday! DOH! There's some good stuff in there, but probably nothing that isn't covered in Wednesday, 1/22 lecture. *sigh* Things were pretty laid-back, and I think the 4 over-achievers who showed up got something out of it (starting with my apology).

    I'm sorry that I didn't record the lecture. I try to reduce the length of recordings by pausing the recording and then re-starting it, as needed. I just messed up the first day. :o(

• 1/22 Notes
• 1/22 Video
  • We had a half-decent informal orientation for everyone on the actual first day of class!

    We defined radian measure and showed its relationship to arc length. We got a rough idea of the quadrant angles as decimal radians, relating them to better-known degree measure:
    1.57 <-> 90 degrees, 3.14 <-> 180 degrees, 4.71 <-> 270 degrees, and 0 <-> 6.28 <-> 0 degrees or 360 degrees.

• 1/27 Notes
• 1/27 Video
  • We covered the 5 triangles that should carry you through the whole semester, instead of trying to memorize the 12-point unit circle. Good stuff. Ask me about it, next time.
• 1/29 Notes
• 1/29 Video
  • Worked a version of WA#2 #1, using period to help evaluate a trig function of a large angle (bigger than 2Pi).

    Worked a version of the "height of the mountain" question.

    Found the values of the 6 trig functions of a point on the unit circle. Didn't mean to, but worked the same version as WA#2's. This is one I had to explain twice, because I was sharing the wrong screen! DOH! Thanks for the heads-up Alexis!

    Discussed even/odd, briefly.

• 2/3 Notes
• 2/3 Video
  • Week 2 Late Edition open until Friday. I will open up another version of it after I upload solutions. The 2nd version will be for 30% deduction. The first version (of Late Edition) will be no deduction until I upload.

    Hope that makes sense.

    To "see" an angle in radians, I always convert to degrees via (180 degrees/Pi) = 1.

    Discussed radians being unitless.

    Drew the 5 triangles I want you to memorize, for 0, 30, 45, 60, and 90 degrees (and their Pi-radian versions). With those 5 in Quadrant 1, you can find trig functions of any angle, with terminus in any quadrant, via the REFERENCE ANGLE.

• 2/5 Notes
• 2/5 Video
  • We covered a lot of topics, relatively informally, related to Week 3 Written Assignment.

    Reference Angles, Solving trig equations, drawing the 2 pictures for a trig equation, finding the OTHER solution (The calculator only "sees" one of them.

    I never mess with inverse cosecant, secant, or cotangent. I just always turn statements about them into statements about sine, cosine, or tangent, and I know how to solve sine, cosine, and tangent questions.

    We didn't do a tangent question. Just a sine and a cosine. Ask me about tangent, next time, if you want to see it. Ordinarily, I try to avoid talking all hour. *sigh* Students like when I do, but that's because of years of training for American-style classes, when we're trying to run a "flipped" class.

    It's not that I don't love to talk all hour. It's that everything is pretty much covered in the homework videos, so why bother you twice? Not the best use of your time, to my mind.

    I'd get what I could from the homework videos and (especially the) notes. Use the face time with teacher to ask questions that the on-demand resources didn't quite do well enough for you. That way, ALL your math time is "on-demand" time.

• 2/10 Notes
• 2/10 Video
  • We did some cosine and sine modeling. Discussed the general graphs of sine and cosine.

    We talked a bit about inverses and the IMPORTANCE of drawing pictures for every trig situation.

• 2/12 Notes
• 2/12 Video
  • We covered inverses of sine, cosine, and tangent. We graphed inverse sine and inverse tangent. We graphed cosecant and cotangent, bootstrapping off graphs of sine and tangent, respectively.

    We talked about the restrictions placed on the domains of sine, cosine, and tangent to keep them 1-to-1, and hence make their inverses functions that spit out one number for a given trig ratio. The key to using the calculator is knowing what the picture looks like, so DRAW THE PICTURE!!!

    Domain of the function is range of the inverse
    Range of the function is domain of the inverse.

    We talked about interpreting the mindless output of your calculator when solving a trig equation.

    We talked about standard math shorthand.

• 2/17 Notes
• 2/17 Video
  • Today was optional lecture day, due to Quiz 1, to give people a little breathing room. I prepped a lot of different things, like "How I score assignments" that didn't get covered. Check out page 1 of today's notes for some insight. If you've been turning in your written work, then you already have a good idea what I'm looking for.

    We worked a couple of application problems, today. I drew a lot of triangles, which is what I want you to start doing, now that you're recovering from Section 1.2, which is all unit circle stuff and more complicated than it needs to be.

    I copy-pasted all the questions from Weekly 1 and 2 into today's notes. I used very little of it. But we did get to look at a couple of the more complicated homework questions, one of which I flubbed towards the end, as Alexis pointed out to me after class. I dropped the "35" in the numerator (Lots of "35"s running around in this exercise.). Anyway, I fixed the notes and uploaded them.

    Thanks, Alexis!

    People who missed today's class: Just scroll through all the extra stuff in the middle. The two application questions are near the end.

    Still trying to teach people to use the resources I slaved over, to make their learning more efficient.

    We did the "Where is the fire?" question and the "Build a cosine function" question. I also built an equivalent "Build a sine function" question. You just have manage where to "start" to get the horizontal shift correct. Sine starts at its midline. Cosine starts at its maximum.

• 2/19 Notes
• 2/19 Video
  • I shared a Calculus I student's take on my "5 triangles" concept. He had the lights go on when he saw what I was doing, and tore the dratted 12-point unit circle off of his wall. Unit circle is all well and good, but you want to think in right triangles in different quadrants whenever you're given an angle or a trig ratio.

    Cofunction Identities - a graphical "proof" of one of them.

    Reciprocal Identities, Pythagorean Identities, ...

    Factoring trigonometric polynomials. Gave the class a quick intro to the Sledgehammer method of factoring, using the Quadratic Formula.

    Trigonometric Substitution revisited. It's not hard if you draw triangles. It's very hard if you never draw pictures.

    The most frustrating thing for me when I teach trig is all the students who try to do the work without drawing any pictures. If you don't draw pictures, you don't see it. If you don't see it, you can't really do it for real. You can do some of it, but a lot of it will just fly right over your head.

• 2/24 Notes
• 2/24 Video
  • We discussed Sections 2.2 (Proving Identities) and 2.3 (Solving Trig Equations). We'll do some 2.3 Wednesday and wrap up with Section 2.4 (Sum and Difference Formulas). I don't teach the difference formulas. I teach the sum formulas. You get the difference formulas from the Sum Formulas. Just replace "y" by "-y" in sin(x + y) and you get sin(x + (-y)) = sin(x - y).

    From sin(x + y) = sin(x)cos(y) + sin(y)cos(x), we obtain
    sin(x - y) = sin(x)cos(-y) + sin(-y)cos(x) = sin(x)cos(y) - sin(y)cos(x) = Difference Formula. So just remember the sum formula and also remember that sine is odd and cosine is even.

• 2/26 Notes
• 2/26 Video
  • We discussed Angle Sum formulas from 2.4 and dipped into Double-Angle and Half-Angle formulas from 2.5 (next week).
• 3/3 Notes
• 3/3 Video
  • We discussed 2.5. Emphasis on Double-Angle, Half-Angle, and Power-Reducing Formulas. I gave credit to the sum-to-product and product-to-sum formulas, although I don't emphasize them on tests. You WILL need the product-to-sum formula in Calculus II, to evaluate some otherwise intractable integrals, but I haven't seen a ton of problems that need the sum-to-product formula, even though it is very useful for something like sin(3x) + sin(5x) = 0.

While I don't require your undivided attention during lecture, I do hold everyone accountable for anything that appears in the lecture notes, as I consider the lecure notes a rich resource for Weekly Written Work and especially Written Midterm and Written Final. questions.

I don't think it's too hard to keep yourself apprised of what we're doing in class. Just check in, open the day's notes, and see what was covered. If need be, you can then open up the video for that day, and scroll ahead to the point in the video where I talked about what I was putting on the board.

That said, if you devote yourself assiduously to doing the work, and doing the work in such a way that you're learning the stuff, and getting all your questions answered, you might not even have to check the notes in order to earn a good grade. But there will be Easter eggs sprinkled throughout, so I'd advise at least skimming each day's notes. That may not take you more than 15 or 20 minutes per week, while you spend the rest of your time actually working problems.

The #1 and #2 strongest correlates with a high grade are:

1. The number of exercises you do over the course of the semester; and,
2. The amount of time you spend working exercises and practicing, especially practicing "without a net," in other words, to perform well on tests, you need to practice working exercises without opening your book or referring to your notes.