We will generally be on-pace or ahead-of-pace with the WebAssign and Written Homework schedules. I encourage and foster your learning to look at the material well ahead-of-time. If you've already spent 15 minutes on the new section before I launch into my tirade, you will find that you learn faster and deeper in less total time.

I do like my job, but part of my job is helping you train yourself to not need me!

• 4/08 Notes
• 4/08 Video
  • We defined the projection vector for 2 vectors u and v. We used vectors to find the interior angles of a triangle.

    I put an emphasis on Written-Work-type exercises in today's talk.

    Still soldiering on with a more or less traditional lecture, with a very reticent cohort. When in doubt, I just plow ahead.

• 4/06 Notes
• 4/06 Video
  • I posted a correction to the last example from the last lecture. The theory was OK, but the execution was poor.

    Then I worked another type of hanging-weight problem, where the information given was in lengths rather than angles. This made it seem more difficult, but it actually handed us the sin(θ) and the cos(θ) needed.

    Then I forged ahead, even though I know everyone's working on their 3.3 or their 3.3 Applications or their Week 8 Written Assignment, today. We'll have the theory all laid out for us on Wednesday to finish Chapter 3 with proj_vu, and College Trigonometry's preview of the Gram-Schmidt Orthogonalization Process.

• 4/01 Notes
• 4/01 Video
  • Today was introduction to vectors and an attempted application. That system of equations I failed to solve at the end was all set up to eliminate the y's without any work. Being a mathematician, once the math is handled, my standard procedure kicks in, and in this case, taking a step back would've made me notice that the y's would cancel just by adding the two equations together! *sigh*

    I suppose you can learn something by watching me flail around, but what an inefficient way to go about solving the system of equations. For linear systems, I teach starting at the top left and working your way down and to the right. In College Algebra, students who look for the trick I missed in class, today, tend to go around in circles, if they start by eliminating y before .

    Maybe the best lesson is to take a step away from your work (or at least the current problem) when things aren't going very well, and come back to it, 5 or 10 or 100 minutes later. I saw the issue within about 30 seconds of class ending.

    I think I will probably try to push back Section 3.4 a few days. Right now, 3.3 I and II are both due this coming Monday.

• 3/30 Notes
• 3/30 Video
  • We proved and then applied the Law of Cosines.

    The book has a long recipe for using Laws of Sines and Cosines, but my approach is "Be aware of 'ASS' situations, which can have 0, 1, or 2 solutions. For the rest? Use Law of Sines when you can, because it's less work. Use Law of Cosines when you must. Rather than have a checklist, just TRY the Law of Sines. If there's not enough info, you won't be able to find all the pieces you need for Law of Sines, and you resort to Law of Cosines.

    The only OBVIOUS "Law of Cosines" situation is when you have a "SSS" situation. We worked one of those. It went: Law of Cosines for one angle. Law of Sines for one of the other angles. The 3rd angle is found by subtracting from 180^o.

    Next time, we'll field questions from Section 3.2, and proceed to VECTORS in Section 3.3.

• 3/25 Notes
• 3/25 Video
  • I proved the Law of Sines for 2 acute angles A and B, but I didn't bring the obtuse angle C, although I was tempted. I decided it made things more complicated than necessary. It's enough to show you the main (easier) part of the proof.

    Then we covered the 3 possibilities in an Angle-Side-Side (or ASS) situation. I think I used the wrong numbers on the 3rd case, although the method was otherwise sound enough. I'll try to clean that up and hit you with Law of Cosines on Monday.

    We never quite got to Product-to-Sum Formulas.

• 3/23 Notes
• 3/23 Video
  • LOTS of identities, today! We covered most of Sections 2.4 and 2.5. Angle-Sum Formulas, Double-Angle Formulas, Half-Angle Formulas, Power-Reducing Formulas...
• 3/09 Notes
• 3/09 Video
  • After scurrying to find the graded Week 04's, we did a bit of review, at breakneck speed.

    Midterm is Wednesday, March 11th, from 10 am to 6 pm. Test takes 2 hours. Bring pen/pencil, scientific calculator, and photo ID.

• 3/04 Notes
• 3/04 Video
  • We went over Week 03 Written Assignment questions, with an eye on the Midterm.

    I was asked at the end about cheat sheets. You may have one page, 2-sided, or two pages, 1-sided, with any formulas you wish.

    I hope that we are all now drawing pictures for trig(θ) = a/b.

• 3/02 Notes
• 3/02 Video
  • We worked some 2.3-type questions (Solving trigonometric equations). We will delve more deeply into the WebAssign questions, which are quite varied, but not what I emphasize on written homework and tests.

    On the Midterm, I'll be very clear on whether I'm looking for exact answers or rounded answers. When I ask for all solutions, that will be the "+ 2nπ" or "+ 360^on" situuation. I'm hoping everyone gets comfortable with the reference angle θ' for a given angle θ, and how to incorporate θ' into final answers.

• 2/25 Notes
• 2/25 Video
  • We did a lot of algebra, today, starting with the principle sqrt(x²) = | x |. The big application, for us, is that
    sqrt(sin²(θ)) = | sin(θ) |.

    I worked some factor-the-trigonometric-expression questions. Factoring skills are helpful, but when in doubt, the SLEDGEHAMMER method for factoring quadratic expressions, where you clobber it with the quadratic formula, makes things a lot easier.

    The above skills will be crucial for solving trigonometric equations. We'll have quadratic equations that are quadratic in sine, cosine, tangent, etc., instead of just x. Equations like

    sin²(θ) + 3sin(θ) + 2 = 0. As in Section 2.2, we'll factor the left hand side (or using the quadratic formula or completing the square) to solve the equation in Section 2.3.

    Factoring the above equation, we obtain (sin(&theta/) + 2)(sin(θ) + 1) = 0. This gives

    sin(θ) = -2 or sin(θ) = - 1, but sin(θ) = -2 is impossible. (sin(θ) > 1). That's an extraneous solution for sin(θ).

• 2/23 Notes
• 2/23 Video
  • Organizational:
    I think the schedule is a bit too slow for this part of the semester. I'd really like to push the pace ahead of lecture schedule for Sections 2.1 - 2.3, so that we can spend more time on 2.4, 2.5 and Chapter 3. I think they're more challenging for students and tested over very thoroughly; whereas, all the identity stuff, while good practice, isn't a huge part of the written testing.

    I don't intend to test beyond Section 2.3 on the Midterm (right before Spring Break). Oh, I'll put some bonus from the later sections in there, but the straight-up Midterm will be based on everything up through Section 2.3.

    Lecture:
    We discussed a few identities questions, and how the WebAssign is less than ideal for these kinds of questions.

    I showed how to use Desmos for those "Use a graphing calculator's TABLE feature to fill in the table" questions.

    I never defined "identity," sadly. An identity is an equation that is true for all values of the variable in the domain of the equation. All other equations are either conditional - true for some values of the variable - or inconsistent - false for all values of the variable in the domain.

    sin(x) = sin(x) - Identity
    sin(x) = cos(x) - Conditional. True for all x = π/4 + n π (where n is an integer.
    sin(x) = 3 - Inconsistent.

    We discussed trigonometric substitution. If you draw the triangles and understand Pythagorus, these are deceptively easy. If you don't draw the triangle, these are very complicated. This will also be true in Calculus II.

• 2/18 Notes
• 2/18 Video
  • Nothing really new in Section 1.8, except all the things I didn't mention, like bearings being measured in degrees clockwise from due north, or some directions being measured so many degrees east or west of due north. I worked a few examples from Section 1.8.

    I sprayed all the 2.1 identities in one big chunk on the board. Pythagorean Identities, Reciprocal Identities, Cofunction Identities. The one people don't remember as well is the one for tangent and secant (and cotangent and cosecant), but they're both basically the same:

    sec²(θ) = tan²(θ) + 1

    csc²(θ) = cot²(θ) + 1

    The coolest thing was the sledgehammer method for factoring quadratic polynomials. If you know the zeros, you know the factors, and this allows you to reverse-engineer the factored form of ANY quadratic trinomial!

    That last bit is from Section 2.1 Part II, which will occupy most of our attention on Monday.

    We're getting a bit ahead of schedule. I think that's good. I don't think my schedule is perfect, and I'd like to build some slack into it, so we can slow down, as I think we will WANT to do in Chapter 3. I can leave the due dates alone, but I highly recommend working ahead of it. You'll want more time to really understand VECTORS.

• 2/16 Notes
• 2/16 Video
  • We finished the Inverse Trig Functions talk, for 1.7.

    We discussed that Week 3 #7 problem that I decided to make bonus.

• 2/11 Notes
• 2/11 Video
  • We started with a "Fit a cosine function to the temperature data" question, discovering that the WebAssign is pretty arbitrary in its persnicketiness (Is that a word?).

    Then we launched into Inverse Trignometric functions, by defining function, 1-to-1 function, and showing some of the issues with functions that are not 1-to-1, when we're trying to build/derive inverse functions for them.

    Then we solved some equations using inverse sine (arcsine), and discussing what the restriction we made on sine to keep it 1-to-1 controls what the arcsine function spits out. I think I got a little ahead of myself, maybe, but I think you should immediately see how the stuff works for solving equations involving sine, to motivate the lesson and help it sink in.

    But what do I know? I never wrote a math book. I just teach the stuff.

    Next up: Inverse cosine and inverse tangent.

• 2/9 Notes
• 2/9 Video
  • We graphed sine and cosine to derive graphs of the other 4 trig functions.

    We covered graphing a transformed sine function by College Algebra (precalculus) methods of shifting, stretching, and reflecting.

    We finished up with some discussion of couple of the Week 3 written exercises.

• 2/4 Notes
• 2/4 Video
  • We discussed organizational matters, trying to study ahead (even if it's just to skim and jot down some formulas).

    I worked a last example or two from Section 1.4 and discussed the most efficient use of the resources:

    Don't view the resources, here, as a LAST resort. They're meant to speed up the learning curve for you. If you feel it's "cheating" to see what I did and hear what I had to say, then practice more problems of the same type, either with the "Practice Another" button in WebAssign or by looking up similar problems in the Exercises in the eBook.

    Life is too short to spend an hour trying to figure out every new wrinkle.

    We finished with graphs of sine and cosine, and how to build sine and especially cosine models to fit data that looks sinusoidal (wave-like). Amplitude, start point, period, midline.

• 2/2 Notes
• 2/2 Video
  • We did bits of 1.3, 1.4, and 1.5. I try to avoid locking you in to the "baby steps" in the book, although I understand the pedagogy of what they're doing. The problem with that "good pedagogy" is that students think they understand things to greater depth than they actually do understand. I say this because of the number of students I see on Midterms, who are still stuck in Quadrant I.

    I apologize for doing that, but I think you'll be better off in the long run, and I'm always about the longer run, sometimes to my dismay. Don't do as I did, planning for the future and not living for the present, as well. If you wait 'til you're "ready" to get married and have kids, for example, you never will! In the context of your math learning, however, I never want today's lesson to put a ceiling over what you can learn, tomorrow, even if it makes it easier to just "get through" today's lesson.

    So, the pedagogy, so far, has been a bit nonlinear. From this point forward, however, I think we can just plod forward without any dain bramage being inflicted.

• 1/28 Notes
• 1/28 Video
  • We were all over the place, today, because, as usual, I love/hate Section 1.2, and I want you to embrace drawing pictures and looking at triangles, rather than referring to the 12-point or 16-point unit circle(s), and making life much harder on yourself in the long term.

    Good questions, today. I think they helped clear some things up, and re-focused the discussion where it was needed, rather than just my "plan" for the talk.

    We touched on inverse sine and inverse cosine, briefly, in the context of drawing pictures, because your calculator will only ever give you half of the picture. It will only spit out one number, when the picture always reveals a second triangle (second picture) and a second number any time you face sin(x) = something. This is because for inverse sine to be a function, it can only ever spit out one number when it is fed one number.

    Key concept: Reference Angle.

• 1/26 Notes
• 1/26 Video - We finished Section 1.1 and barely got started on Section 1.2.
  • Sorry about the nonexistent Studen Guide for WebAssign on that first "Intro to WebAssign" assignment. I'll check with Cengage, to see what's happening, there. Maybe I left it out in the setup. I know I'm a little hesitant about the Study Guide, because you can waste a lot of time doing what THEY want, while falling behind on what I want.

    Don't hesitate to slow me down if things are jumping back and forth too rapidly. I get excited about what I want to show you, and want to avoid wasting time, so as little fiddling around time is sort of my goal. If serving that goal makes learning more difficult, that's messed-up.x

• 1/21 Notes - Orientation
• 1/21 Video - Orientation
  • E-Mail Settings, Register for WebAssign, Use WebAssign Features, Use harryzaims.com resources, Written Work.

    Man oh man! About everything that could go wrong, did go wrong! Great first impression I made! Woo-Hoo!

    I think I got the gradebook thing fixed. Click here for your personal grade report

    We tweaked some of the due dates, already. I really try to push 1.1 getting done, early, so we can relax towards the end of the semester. Hit the ground running, and be strong and unhurried in May.