Parametric Addendum

Given that it was tough giving Parametric equations enough time in class, I am changing the first assignment on parametrics to section 12.3 of the Brown book.  Do the following problems on pages 437-439/23-29, 39, 40.  This is our new Day 3.

Polar Coordinates

This is a quick but interesting unit on another way of describing the location of points in space.  It is a somewhat surprising application of trig that can also be used to work with complex numbers.  The schedule is plagued by holidays and MCAS but we will work around it as best we can. Polar coordinates are covered in the Demana book in sections 6.4-6.6 and in the Brown book in Chapter 11.  I am using Day1 notation rather than dates because the E-Block and G-Block sections will be off (due to the half day - but not if there is a snow day on the 7th!).

Day 1    Intro to Polar  CW Brown p.400-402/1-11 odd
            HW Demana p.492-493/5,6,23-30,52-54,61,63
Day 2    Converting equations and graphs (polar <=> rectangular)
            HW D p.500-502/5,7-13,17,21,23,45,49,53,55
Day 3    Parametric Equations 
            HW B p.437-439/23-29, 39, 40
Day 4    Parametric Equations some more
            HW Worksheet
Day 5    Cylindrical & Spherical Coordinates  
            HW Worksheet
Day 6    cis, Products of Complex Numbers
            HW B p.406-407/10, 12, 15, 17, 24-31 and D p.512/63 (derive Quotient Rule)
Day 7    Powers and Roots of Complex Numbers (De Moivre's Theorem) 
            HW B p.410-411/4,5,9-14 and p.413/5,6,8,11-13
Day 8    Extra Practice 
            HW finish worksheet
Day 9    Review
Day 10  Polar Test (could be 3/25 for E-Block, 3/26 for G-Block, neither date is optimal - see below)

Important Dates

3/07  Professional Development Half-Day C B H F

3/19  MCAS Day 1 (Hr G H B)

3/21  MCAS Day 2 (Hr G H A)

3/22  MCAS Day 3 (D E F B C)

3/25  1st night of Passover

3/26  2nd night of Passover

3/28  End of Term 3

3/29  Good Friday - no school

Sum and Difference Links

There are several resources to view proofs of the angle addition and angle subtraction identities.  Look them over and make sure you understand them.  You will be required to prove some of the basic identities on your test and the proofs of these identities require diagrams which may not occur to you during a test situation if you haven’t thought about them before.

Demana Precalculus 5.3 page 421 (a distance formula based proof)

Brown Advanced Math 10.1 p.369 (a law of cosines based proof)

Mr. Richardson’s PowerPoint presentation

            download here

Another website with very elegant triangle proofs:

            http://www.cut-the-knot.org/triangle/SinCosFormula.shtml  and

            http://www.cut-the-knot.org/triangle/SinCosFormula2.shtml (beautiful!)

Trig Identities

Lots of Proofs this unit! We start with simplifying practice and then jump in.

Note: We will be using the Demana book for most, but not all, of the assignments.

2/12   Trig Identity basics

          HW D p.410-411/3-60 by 3's, 69-73 odd

2/13   Simplifying for a solution

          HW D p.411-412/52-62, 75-82, 85

2/15   Proving Trig Identities

          CW D p.418/11-33 odd

2/16 - 2/24 February Vacation

2/25   Recap and More Practice with Trig Identities

          HW D p.418-419/35-51 odd, 52-60, 71

2/26   Review all, Sum and Difference Formulas

          HW D p.425-427/3,5,7,13,17,21,27,29,31-35,37,43,45,47,48,52,55,73

2/27   Double Angle, Half Angle and Power Reducing Formulas

          CW B p.374/39-41, p.385/45-47

          HW D p.432/3-30 by 3's, 39-45 odd, 53

3/01   Review and Extension Problems  CW Worksheet

          HW B p.384-385/3, 5, 52, 53 and p.390-391/23, 26-28, 43, 44

3/04  More Practice
3/05  Trig Identities Test

Dealing with the Test/Snow Day

The test will happen on Monday, February 11th due to the snow day.   You may email me this weekend if you have questions.

Geometric Trig

Post-test homework was to do the area and identity worksheet. We continue with the more geometric applications of trigonometry. For this unit we will use primarily the Brown book.

1/28  9.2  Area Formula and applications

                HW p.342-344/1-19 odd, 20-22, 35, 36

                (p.344/34 is a bonus problem - turn it in for extra credit)
1/29  9.3  Law of Sines

                HW p.347-349/1-27 odd

1/30  9.4  Law of Cosines

                HW p.352-354/1-17 odd, 22

2/01  9.1 - 9.4  Mixed Trig Problems

                HW p.337/31-33, 37;  p.349/28;  p.354/23 and p.356-358/11,14,18,21,24,25

2/04  9.4  Mixed Trig Problems

                HW p.357-358/29-37
2/05  9.4  Mixed Trig Problems
                HW p.358/38, 39, 40, 42

2/06  Review and Extension Problems (Practice Test/Answer Key)

2/08  Test of Geometric Trig

The Geometric Trig test will have questions that require a full understanding of the trig area formula, the Law of Sines, and the Law of Cosines. There will be one problem (chosen by me) from the "C" problems on page 358 (not 41 or 43). I have not assigned every problem in the unit but notice that after you finish these problems you should be able to find the area, the sides, the angles, the length of the median/angle bisector/altitude, and the radii of the inscribed and circumscribed circles for any triangle - among other things.

The beginning of Trig...

Trigonometry is our longest unit spanning more than two months and three tests. We start in the Demana book but will move into our second book, the Brown book, as we progress.  We begin with Right Triangle Trig, mostly review from last year.  

12/12  4.1 Angles and their measures

           HW p.325-328/3-39 by 3's, 44, 46, 52-56, 72-74

12/14  4.2 Right Triangle Trig

           HW p.335-337/1, 7, 16, 19-23 odd, 59, 60, 61, 63, 66, 73, 75-78

Circular functions (4.3) are a big part of understanding trigonometry conceptually. We will spend a few days making sure you understand. Problems 67-76 on 12/17 are the problems you should really push yourself to understand - don't just give up and wait for me to go over them.

12/17  4.3 Circular Functions
           HW Demana p.347-349/2,3,7,27-35 odd, 41-53 odd, 60-64, 67-76;

12/18  More Practice CW Brown p.272/3-10,  13, 14 and worksheet
           HW Brown p.272-274/17-27 odd, 29-32, 33-41 odd

12/19  Finding all solutions with circular trig HW finish handout

12/21  Quiz of 4.1-4.3 and game

12/22 - 1/02 Christmas Break! (Parent Conferences on 1/02)

Sinusoids are some of our 12 basic functions, period functions with repeating patterns. We will be spending time before and after vacation on this topic. There will be a quick skills quiz.

1/03  4.4 Graphing Trig Functions handout (G-Block in class, E-Block for homework)

1/04  4.4 Sinusoids
         HW Demana p.357-358/13-41 odd, 42, 49, 50, 53, 73, 75

1/07  CW p.360/91-97   HW p.357-359/51, 52, 54-57, 59-69 odd, 70-80 even

1/08  Trig Evaluation Practice and Extra Problems

         HW finish problems 1-12 of Extra Problems worksheet

1/09  Discuss Extra Problems Worksheet (and Professional Developement - Half Day (B A G F))

         HW finish Extra Problems worksheet (13-21)

1/11  Solving with Sinusoids  CW problems 1-5 (answer key)

         HW problems 6 - 9

1/14  Continue Solving with Sinusoids

         HW finish rest of handout, problems 10 - 17

1/15  Quiz of 4.1-4.4

1/16  4.5 Graphs of the other Trig functions and 4.7 Inverse Trig functions

         HW p.366-368/13-16,18-39 by 3's,43,60,63,64 and p.385/37-40

1/18  Extra Sinusoid and Inverse Trig Problems (and End of Term 2)

         HW in Brown: p.290-291/11-14, 27-29, p.306-307/30,31,33,36, p.314-316/15,17,18,21,25,26

1/21  Martin Luther King Day - no school

1/22  Review (answer key)
1/23  Practice Test (answer key)

1/25  Test of Ch 4
         HW Trig Area and Identity intro