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# PRECALCULUS

10/22–pg. 653: 3-33, multiples of 3.

10/19–pg. 306 (old book), 19, 20 (a-c); we will do probs similar to 21-26 in class Monday (the latter require a calculator and the application of inverse functions).

10/18–Major or minor assignment tomorrow on graphing, please bring you graphing calculator.

10/17–pg. 305 (photocopied, old book): 11-16 plus text pg. 358, 74-76. Minor assignment on graphing Friday, 10/19

10/15–As per your request, we will finish going over hwk assigned on 10/12. In addition: pg. 358: 72, 73

10/12–Handout: application of sinusoids, 1-7 (use graphing calculator; adjust window as needed).

10/11–Teacher absent; special assignment given

10/04–Chapter Test tomorrow

10/03–Handout: 52, 60, 61,75-78

10/02–Tomorrow we will look at transformations of tan, cot, csc, and sec graphs…HWK pg. 395 (8, 16,22–similar probs will be on your next major assignment Friday)

10/01–In the handout from the Sullivan book (pg. 595): 67-73

9/28–Test on Monday…there are a few questions on graphing although you won’t have to graph.

9/27– As per Ms. Russo’s suggestion, no homework tonight due to Open House tonight.

9/26–Read 352-353; do 1-6 pg. 357 (How do we obtain the graphs from the parent function, y= sin x? What is the new range? )

9/24–Check portal for graded minor assignment administered this morning..need to review a few things before our major assignment tomorrow.. Please review inverse trig functions as well as the graphs of all trig functions including domain, range, continuity, even/odd, etc.

9/21– Study guide(Chapter 7 review, old book). Minor assignment on Monday, 9/24; major assignment (similar to your study guide) Tuesday.

9/20–pg. 385: 1-12–Remember that inverse sine(x) and inverse tan(x) will yield a negative answer if x<0; positive if x >0. The inverse cos(x) yields an angle in Q2 if x<0. Remember that inverse trig functions are restricted to two quadrants and we are not dealing with the whole unit circle–there are no answers to inverse trig functions in Q3. Review the graphs, domain and range. See summary of graphs on pg. 399.

9/19–You did not have questions about the hwk assgn given yesterday which makes me suspicious as to whether you did it..You probably will see a similar problem in a major assignment next week. For tomorrow: Reread 4.7, paying attention to the inverse tangent and inverse cosine graphs (how are they restricted? Domain, range? Why is the inverse cosine restricted from 0 ≤ y ≤ π? Why is the inverse tangent restricted from -π/2 < y<π/2 (compare with the inverse sine)). For homework; pg. 395 22, 25

9/18–Read 4.7 –“Inverse Trig Functions”–pay close attention to highlighted material; we will be discussing this topic for the next two days.). Written homework:

pg. 394: 8, 15, 16

9/17–Handout: 93, 94

9/14– Handout: 79-90

9/13–Handout: 31-24, odd. Minor assignment tomorrow: You are expected to know the following: the sign of a trig function depends on the quadrant in which the terminal sign of the angle lies;. Reference angle (example: express the sine (-310 ) in terms of its reference angle. Solution: terminal side in in quadrant I (negative rotation); reference angle (-310º – (-360º) or 50º, so sin (-350º)= sin (50º). If sin 350 = – sin 50. Why? B /c 350 is in Q4, and the sine is negative in Q4, but all reference angles have positive trig values since all reference angles are in Q1. Also, trig values of special angles 45, 30, 6o and their multiples. Also, if given a trig function in a certain quadrant, find the remaining five functions. I have been discussing degrees in this blog, but you will have radians as degrees on your assessment tomorrow.

9/12-Handout: 9-30–The purpose of these exercises is to reinforce not only the trig values of special functions, but reference angles, odd/even relationships (remember only the cos and its reciprocal are even functions, i.e., symmetric with respect to the y-axis f(-x) = f(x) look at the graph; the other trig functions are odd); Pythagorean relationships (sin²θ + cos²θ = 1 which can be manipulated to yield other relationships), cofunctions (#24) and reciprocal relations (23). DO NOT USE A CALCULATOR–doing so defeats the purpose of the assignment + you will not have a calculator available for your assessments. However, I encourage you to use your handouts and notes. Review the cosine and sine graphs (domain, range, even/odd, continuity, periodicity).

9/10–pg. 349: 67-74

9/6–Read 4.4 (pp. 350-351) Basic Functions: The Sine and Cosine Functions-graph them in your calculator--make sure you are in radians! (y1= sin x; y2=cosx), Zoom 7, check your window (you may want to restrict it to one rotation to match the unit circle). Where does it cross the x-axis (angle), what are the max/min values? Compare to the unit circle.. Graph y1 and y2 simultaneously..where do they intersect? Where is the sine graph increasing? decreasing? answer same for the cosine. Where are both sine and cosine negative? positive? We have a lot to talk about.

8/31–Expect pop quizzes on the unit circle and trig functions of special angles daily. Hwk: Handout, 42-74, even (you may use any short cuts discussed in class this morning (e.g., reciprocal relationships, Pythagorean relationships (sin ²θ + cos²θ = 1, or any variation as discussed in class this morning). The idea is for you to feel comfortable using the unit circle…Remember the mantra: All answers are in the unit circle!

8/30–Hwk: Handout, 41-73 (odd nos.)–What is the purpose of this assignment? Reinforce trig values of special angles (use unit circle if needed, quadrants, reciprocal relationships..FYI: (sin θ) ² is written as sin²θ ; in your calculator is entered as sin (θ)².

/29–Complete handout given this morning (unfinished homework quiz) + pg. 348 (text) 43-48 (good probs..in what quadrant is the angle in question? )

8/28–Hwk: photocopied pg. 279, Written exercises 1-4–state whether ans is + or neg. What relationship is there between a given angle θ and any angle coterminal with θ? Tomorrow we will go over pending hwk assignments ( 8/23 and 8/24 as well as the hwk given today) before your hwk quiz. ALERT: PLEASE REVIEW UNIT CIRCLE AND TRIG VALUES OF SPECIAL ANGLES, PARTICULARLY QUAD I (INCLUDED IN NEXT MINOR ASSIGN, FRI).

8/27–Go over notes and worksheet given this morning..We will go over the hwk assignment given Fri (see below).

8/24–pg. 347 (3+4=7): 25-42 (see if you can answer without using the unit circle–reference angles (Hint: Look at the denominator if in PI radians; also consider the quadrant to determine the sign).

8/23–Review the unit circle (hand out–pay attention to special angles). Hwk: pg 383, 3-20 (even)

8/22–Read pp. 330-332 (“Two Famous Triangles” aka 45-45-90 (right isosceles triangle) and 30-60-90..these triangles form the basis of your journey in trigonometry) as well as section 4.3 (“Trigonometry Extended: The Circular Functions” (SOCAHTOA goes circular!)) Bring hand out tomorrow!.

8/21–photocopied pg. 266: 19, 20

8/20–A couple of you had questions about #13 (“rpm” means “revolutions per minute”, i.e. the number of rotations in one minute..one rotation is 36o° or 2π radians). Minor assignment scheduled for tomorrow: convert degrees to radians, area of a sector, arc length, (Key: Θ = s/r). Will go over 13-15 tomorrow before the quiz.

8/17–pg. 265–(photocopied)–11-15

8/16–Length of an arc (s= Θr, if Θ is in radians; (Θ/360)* (2πr), if Θ is in degrees). Area of a sector (a sector of a circle is the region of the circle bounded by two radii and an arc of the circle, think “slice of pizza”) If Θ is in radians: (Θ/2)* r² or (sr/2)..Which formula to use? Well, it depends on information given in the problem. Remember: anytime you are using radians, think Π. Homework: pg. 265, 3-10 (photocopied, old book). Maybe quiz tomorrow–converting from degrees to radians and vice versa; co terminal angles. Check your book, 328 #71.

8/15–pg. 335 (x3–this means “multiples of 3”); 29-30, all (follow directions).

8/14–For the hwk, use the formula Θ = s/r (definition of radian measure; formula may be manipulated as needed REMEMBER: Θ MUST BE IN RADIANS in order to use the formula .) , pg. 325–25-33 (odd); 35-38 (# 37 was discussed extensively in class this morning, thanks to Danielle P. who took the initiative to do the prob last night :) )

8/13–pg 325: 1-24 (all; you may use a calculator, although not needed (1-8). For probs 9-16, you want the degrees to cancel, so multiply by (π/180º); for 17-24, multiply by 180º/π, cancelling the π. For #23, “2” means ” 2 radians” (remember that π radians ≅ 3.14 radians–think “unit circle”). See formulas pg. 322

8/10–Read 4.1– Any time you have a reading assignment, pay attention to formulas and the main ideas/concepts (highlighted in blue rectangles), new vocabulary (boldface) as well as the marginal notes (annotations)…Every section begins with “What you will learn about” followed by “why”..(I will not repeat this info going forward)., pay attention to examples (in this case, exs. 1, 2, and 3).

**CALCULUS AB:**

10/22- Hwk: pg. 149: 18-20; pg. 348: 39-46

10/19– Major Assignment Monday! Your test is a work in progress; will finish putting it together Mon morning…what to study? Derivative rules, chain rule, implicit differentiation (redundant, isn’t it? ID includes CR!), definition of the derivative, you will see a couple of homework and classwork probs that we have done (revisited), and yes, Olivia, there are limits (like there are limits to your grade). Mainly multiple choice, but I’m trying to get constructive response, which, hopefully, will not prove to be destructive response ;>) Bonus prob?

10/18 Kha Le’s problems are a good practice/review for the minor assignment tomorrow; I strongly recommend you do it.

10/17–pg. 142: 40, 41, 43, 48 Tia Williams knows how to handle setbacks, positive attitude…fails math and still smiles :) (quoted from her recommendation letter).

10/15–I hope Carter is a better driver than he is a deriver (as evidenced on his last assignment). HWK: pg. 142: 1 thru 7, 10 (compliments of Ms. Helgeson, why?, 12- 16, 24, 27, 28

10/12–Let me be explicit about this: you need to know implicit differentiation…so please read 2.5

10/05–Major Assignment 10/09–(Mainly Ch 2, up to and including Chain Rule)

10/03–9 pg. 136: 90, 92, 100, 101, 102, 104–Last day for Chain Rule. Expect an assessment tomorrow.

10/02–So, I’m here in my room after school grading the homework quiz from this morning when Patrick L and Megan K stop by to talk about college and schmooze (they were supposedly helping Olivia with HSAC planning)…which explains the delay in posting the homework and finalizing your minor assignment for tomorrow. . HW: pg. 134: 77, 80, 81 (second derivatives can get unwieldy, particularly with rational functions (think quotient rule applied twice–&^%#)). Minor assignment on for tomorrow..

10/01–Good afternoon–sorry I’m late–working on implicit differentiation problems at the request of Celia and preparing for the next topic which makes the Chain Rule seem easy (in fact, without CR there is no much we can do and without Implicit Differentiation, what is there to differential calculus).. We are getting better with the CR, but I feel we need more practice, right Noor? So: pg. 133: 47, 53, 56, 58, 61, 64–we will have some fun with probs from Stewart as well…ah, yes, probably a hwk assignment at the suggestion of Kevin Kim. (CR not included).

9/28–Calculus is torture now we are being chained, like in the Chain Rule (I know this is lame)–Minor assignment (20 minutes)–review basic differentiation rules (relax, Muntha’, CR not included). HWK: (good practice for the minor assignment) pg. 133–21, 24, 30, 33, 38, 43, 47

9/27– As per Ms. Russo’s suggestion, no homework tonight due to Open House tonight.

9/26–Be ready for a homework quiz tomorrow. Homework: pg. 115; 91-98

9/24–It is 7:00 PM –How many times have you checked the wiki, Muntha? At least three? Just sayin’…OK…got inspired and decided to change the test a bit…so, here is what is in store: About ten multiple choice questions, a drawing (Ahmed asked..given certain conditions, similar to one we had before0, ∼ 85% limits, open ended questions that you have to explain, probs that you have to work and arrive at a conclusion..Suraj and Neel think it is a good test…yes, derivatives are included. No calculators!

9/21–On Monday we will go over all the hwk assignments pending. Also: hwk on product and quotient rules, pg. 119:–11, 30, 34, 52, 54, 57, 60, 67, 75. Probably have a hwk quiz on Monday. Major assignment on Tuesday.

9/19–pg. 116–101, 102, 107, 111–Eddie and Shivan you can dance (yes, we want an encore-the BEST number in the pep rally, worth my attendance! synchronized and symmetric)..now, can you do calculus?

9/18–pg. 114: 55,61, 66, 76,89,91

9/14–Test Major Assignment Qu’est que nous avons avoir? Make use of graphing calculator to make inferences about a graph (calculator should be in radian mode in this class always (Kevin Kim), limits, continuity, T/F, definition of the derivative, IVT…Email me if you have any questions about the hwk assignments (9/13 and 9/11-.. Read about sum, product and quotient rules.

9/13–pg. 103: I will do 47 and 48 in class; your hwk: pg. 113: 14, 18, 64, 62

9/12-As people in Carolina prepare for Florence, you should prepare for either a hwk participation grade or a minor assignment tomorrow on any topics we have covered so far (yes, Olivia, that includes limits…how can we forget about limits?). I haven’t decided yet on the format…let me look at the archives and suggestions from my cal posse.

9/11- pg. 102-47-49; 66, 70-80; 85, 86

9/10–pg.102: 8, 22, 30, 34, 36

9/6–Read 2.1..tests have been graded and posted!

8/31–Please be on time for your Unit I Test on Limits. What’s on the test? Everything! (only one prob requires trig functions). Every prob has been discussed in class and/or assigned for hwk (some are deja vu). Some you can do by inspection. A couple of probs are AP style in wording or origin. After our class Friday and your two minor assignments, I think you are prepared. Trick probs? maybe 2, but this is a matter of perception…I prefer to say ,”probs that make you think”. No calculators (no need to reduce answers); you must work diligently and write clearly and beautifully! . You will need scratch paper!

Have a nice weekend! Don’t spend too much time studying (Muntha, Noor et al); Happy 16th, Channel (test is my belated bday present to you; now, present me with a good grade). Tia, I think you will find the test doable and tolerable. Celia and Carter, now is my turn to ask you questions. ; > )

8/30–pg. 199: 19-24, 29-32. Remmeber: use dominance if possible or manipulate expression if possible.

8/29–Read 3.5 (again!), paying attention to example 4. You should be able to do 1-14 in your study guide.

8/28–ma tomorrow; MA Friday–Tomorrow continuity and (graphically and analytically), IVT, limits…

8/27–Read 3.5 in your text book ( pp. 192-198) and complete handout given tonight (hwk); use your calculator as needed; we will discuss how to find horizontal limits analytically tomorrow. Start reviewing for major assignment on Friday (more info later).

8/24–Handout on composite functions; minor assignment Tuesday 8/28 (limits and continuity).

8/23–Tomorrow is hwk day..that means we will go over all hwk probs from 8/21-today) add pg. 77: 68, 75, 83, 86

8/22..Add the following to your hwk–57-60 , 69-72; Read about IVT (necessary condition: function must be continuous on an interval).

8/21-Later than I expected (Carter and Celia, pls remind me to do probs 83-84, pg. 66..overdue). Now, for continuity: pg. 76: 13, 14, 25-32; 34-48 (even)

8/17–Homework Quiz on Monday (remember these count for 20% of your grades)..All the probs have been either assigned for hwk or discussed in class, short quiz, I expect most, if not all to well; I think you are ready, don’t disappoint me. I hope to return your graded quizzes Tues so that we may have a minor assignment (a bit longer, 30%) on Wed 8/22 —I will not give you a minor assignment unless I have finished grading the quizzes! Those of you who have had me before know that I like to return assessments ASAP. We will tied up a few loose ends on Mon before the quiz (such as the hwk assignment given on 8/15, how to graph piece wise functions in the calculator (C4, the last prob we did was input incorrectly, which is we were getting only one graph which appeared to be continuous at x= 0; we’ll correct this on Monday (remind me Celia, Olivia or if your name ends in “ia” Tia?)

8/16–Quiz postponed–Monday, 08/20 (sorry to disappoint you,Noor et al, but I’d like to look at a few more problems from other books, and start on “continuity” and piece wise functions).. Suggested by Carter: (use your calculator so that you may have a better understanding): pg. 66: 89-84 (In physics and engineering the algebraic function that multiplies a trig function( either the sine or the cosine, why?) is called the “damping factor” and acts as the “amplitude” (remember graphing y=a sin (x) where “a” is constant? Well, you were doing a variation of the “squeeze”/”sandwich”/or “pinching” theorem (depending on the book you are using–“Squeeze” is by far the most common and logical)–I think I will name it the “Carter Nugent” theorem, at least for now or the “Adrija” Theorem). PLEASE READ 1.4, paying attention to boldface terms and main (boxed off in rectangles).

8/15–pg. 67–101-104 (compliments of Dr. Bouchon ; don’t spend too much time on these problems, however), #122; “Getting at the concept” (95-98).

Tomorrow we will finish going over probs 83-86, pending from 8/14, address the hwk for today and look at how other authors approach ” limits” and work probs from other sources. Quiz on Friday! Don’t despair…yet!

8/14–pg. 66: 67-86

8/13– pg. 66: 56 -62 (care to comment anyone? For those of you who have been reading ahead (or at least have led me to believe that you are reading ahead), do these probs look familiar? )

8/10–Read pp. 50-51; do pg. 55: 9-18 (graphic interpretation); pg. 65: 27-34 ( time to review the trig values of special angles..unit circle, ASTC), 41-44; 49-52