Period 1- Trig Assignments

HOMEWORK FOR
MONDAY 02/01/2010

YOUR FINAL EXAM FOR THIS COURSE
IS ON FRIDAY, FEBRUARY 5, 2010

DO PROBLEMS FROM YOUR
REVIEW PROBLEM SET ON COURTESY HANDOUT SHEET.
(BLUE TEXT PAGE 120 THROUGH 128 ALL PROBLEMS)

COME TO CLASS TODAY WITH QUESTIONS...

HOMEWORK DUE
FOR FRIDAY 01/29/2010

DO PROBLEM 35 GREEN TEXT PAGE 539
(IF YOU DIDN'T FINISH IT IN CLASS.)


DO ADDITIONAL 6 PROBLEMS ON
EXAM REVIEW SHEET (PROBLEMS 6 THROUGH 12)
(THE SHEET IS TAKEN FROM BLUE TEXT PAGE 120-122.)

HOMEWORK
TO BE HANDED IN
ON THURSDAY 01/28/2010

DO PROBLEM 31 GREEN TEXT PAGE 539 AS A CLASS.
(LAW OF SINES-- AMBIGUOUS CASE)

CLASS ACTIVITY
FOR THURSDAY 01/28/2010

CORRECT HOMEWORK PROBLEM
THAT IS DUE TODAY.

DO IN CLASS PROBLEM 33 AND 35, TEXT PAGE 539
HAND IN.

HOMEWORK TO BE HANDED IN
WEDNESDAY 01/27/2010

GREEN TEXT PAGE 539
ODD PROBLEMS 9 THROUGH 19

HOMEWORK DUE
TUESDAY 01/26/2010

DO ODD PROBLEMS 9 THROUGH 19
ON GREEN TEXT PAGE 539

HOMEWORK DUE
ON MONDAY 01/25/2010

EXAM REVIEW PROBLEM SET II.
(PROBLEMS 1-28)
DO AT LEAST 6 BEFORE 01/25/2010

CLASS ACTIVITY
FOR MONDAY 01/25/2010

(1) Introduced Law of Sines.

(2) Worked one example (green text page 537, Example 7)

(3) Assigned practice.

HOMEWORK DUE
FRIDAY 01/22/2010

DO TEXT PAGE 481 PROBLEMS 1 THROUGH 10

(These problems will require your undivided attention for about an hour. Please plan time for your trig homework.)

HOMEWORK FOR
THURSDAY 01/21/2010


READ GREEN TEXT P 473 SECTION 6.4 P 473-474
DEVELOPING AND USING
THE SUM & DIFFERENCE FORMULAS

CLASS ACTIVITY FOR
THURSDAY 01/21/2010

DERIVE SUM & DIFFERENCE FORMULAS ON THE BOARD.

WORK PROBLEMS WHICH PRESENT TYPICAL
APPLICATIONS OF THESE FORMULAS
(1) Derivation: p 473 - 474
(2) Example 1: p 474 using S formula to find exact values of angles
(3) Example 2, p 475 using D formula to find exact values of angles.
(4) Using S & D formulas to derive additonal IDENTITIES
(5) Example 3: p 476 using S formula to find exact values of angles.
(6) Example 4: p 477 using D formula to find exact values of angles.
(7) Example 5; p477 finding exact values
(8) Example 6: p478 derive tan( s + t) formulas from above sine(s + t) & cos(s + t)

HOMEWORK FOR
WEDNESDAY 01/20/2010


STUDY FOR TEST
(on trig graphing + miscellaneous)

CLASSWORK FOR
WEDNESDAY 01/20/2010

TEST (GRAPHING TRIG FUNCTIONS + MISCELLANEOUS)

HOMEWORK TO BE
COMPLETED BY
TUESDAY, 01/19/2010
(following the Martin Luther King holiday)

GRAPH PROBLEMS 31 through 35 on
Page 415 of the GREEN TEXT
(and found on Courtesy Handout
at bottom of page.)

CLASSWORK FOR
TUESDAY 01/19/2010

Work out with the class all
homework problems from
handout text p415, problems 31 through 35.
Display & discuss graphing of trig functions
using the white board.

HOMEWORK DUE
FRIDAY 01/15/2010

DO PROBLEMS 3 through 10 Set 5.4
in GREEN TEXTBOOK Pages 414 - 415
(and provided on photocopy handout as a courtesy to students.)

[ALSO, COMPLETE ANY UNFINISHED PROBLEMS
FROM THE HOMEWORK ASSIGNMENT
WHICH WAS DUE ON Thursday, 01/14/2010.]

CLASS ACTIVITY
FOR FRIDAY 01/15/2010

1. Presented a consolidated 5-STEP
outline of how to graph the general
trig function of the form

y = A sin B( x -C ) + D

2. Used the 5-STEPs to graph
two different functions.

3. Assigned graphing exercises
for be done over the 3-day weekend.

HOMEWORK
TO BE HANDED IN ON
THURSDAY 01/14/2010

DO PROBLEMS
10 through 15 found on Monday's
handout sheet (Blue Text page 119).

YOU WERE GIVEN GRAPH PAPER
ON WHICH YOU CAN DRAW THE GRAPHS
REQUESTED IN THE ABOVE HOMEWORK PROBLEMS..

CLASS ACTIVITIES
ON THURSDAY 01/14/2010

Competed a 5-question Warm-Up
covering the graphing of trig functions
that was included in Examination Review yesterday.

Went over as many
of problems 10 through 15
from last night's homework as
time permitted.

[FOUND the mysterious Ms. Samatha! ]

HOMEWORK DUE
WEDNESDAY 01/13/2010

DO PROBLEMS 8 & 9 ONLY
FROM THE PROBLEM SET
ON YOUR HANDOUT FROM
MONDAY: (BLUE TEXT PAGE 119, PROBLEMS 1-20)

CLASS ACTIVITY
ON WEDNESDAY 01/13/2010

1. We learned that our Final Exam
in Trigonometry will be on
FRIDAY 02/05/2010 in the morning.

YOU MUST TAKE THE FINAL EXAM
TO PASS THIS COURSE!!!!!
NO EXCEPTIONS....
(Plan around your exam obligation...)

2. We went over the answers to last night's homework
problems 8 & 9 on handout (BLUE TEXT PG 119)
using drawings on white board to illustrate why

Sin (180 + THETA) = - SIN (THETA).

3. We took notes & discussed the details
of graphing y = Sin (x), which is the Basic Sine Graph.

And we examined the effects of the parameters

A amplitude
B period Remember P = ( 2 Pi ) / B
C phase shift
D displacement

on the graph of y = A Sin B (x - C ) + D

CLASS ACTIVITY
FOR TUESDAY 01/12/2010

We handed in homework
from yesterday; then students
worked problems 1-5 (out of 7 assigned)
on the whiteboard.

The emphasis was on
forming CONVERSION FACTORS
correctly and CANCELING UNITS
where possible.

The problem converting each
student's age from YEARS
into SECONDS was worked
for 18 years. Emphasis
was placed on FORMING
CONVERSION FACTORS
correctly.

NO ADDITIONAL
PROBLEMS WERE ASSIGNED
FOR CLASSWORK.

CLASS ACTIVITY
ON MONDAY 01/11/2010
(FIRST DAY BACK AFTER CHRISTMAS BREAK.)

DONE IN CLASS & HANDED IN:
Problems 1-7 Blue Text page 119

(The theory required to complete each
problem is presented on the white board.
Each student needs to copy this theory.
Use the given formulas.
Use the given diagrams.
Recall how to create CONVERSION FACTORS)
(You want certain words-the units-to cancel.)

HOMEWORK DUE
TUESDAY 01/12/2010

DO PROBLEMS 1-7
ON HANDOUT PAGE
(The problems on the handout
are EXACTLY LIKE problems
1-7 done in class Monday 01/11/2010)

DO ALSO:
CALCULATE THE NUMBER OF SECONDS
YOU HAVE BEEN ALIVE:
Start with your age in WHOLE YEARS.
Create conversion factors to end up with SECONDS.

HOMEWORK
FOR FRIDAY
12/18/2009

NO WRITTEN HOMEWORK DUE.

CLASSWORK FOR
FRIDAY 12/18/2009
(Last class day before
the Christmas Holiday.)

Classes Resume Monday, January 11, 2010

CONTINUE REVIEW ASSIGNMENT
ON PAGE 119, BLUE TEXT BOOK
PROBLEMS 1-20.

HOMEWORK
DUE THURSDAY
12/17/2009

NO WRITTEN HOMEWORK.

Read development (derivation) of
the next Trig Identities:
cos (A + B) = cosA cosB - sinA sinB
cos (A - B) = cosA cosB + sinA sinB

FOUND ON GREEN TEXT PAGE 473 BOTTOM.

Read through the algebra work
on TEXT PAGE 474 TOP that creates
the above cosine identities for angles A+B and A - B.

CLASSWORK
FOR THURSDAY
12/17/2009

DO REVIEW ASSIGNMENT
BLUE TEXT BOOK PAGE 119
PROBLEMS 1-20
(Do as many as possible.)

HOMEWORK
FOR WEDNESDAY
12/16/2009

TEST ON PROVING IDENTITIES
USING FUNDAMENTAL TRIG IDENTITIES.

CLASS ACTIVITIY
FOR WEDNESDAY
12/16/2009


* * * * * * * TEST * * * * * * *

On fundamental trig identities.

HOMEWORK DUE
TUESDAY 12/15/2009

COMPLETE PROBLEMS FROM CLASSWORK:
The CLASSWORK board problems are actually
the following problems
found in your GREEN TEXT BOOK, PAGE 471,
PROBLEMS 37, 38, 39, 41, 42, 43, 44, 45, & 46
Students can use www.hotmath.com and their school
ID to solve odd problems.

REMEMBER: TEST ON IDENTITY PROOFS ON WEDNESDAY!

BE READY...

CLASS ACTIVITY
TUESDAY
12/15/2009

Identities 5 through 9 from
our last class meeting
were worked on the whiteboard
for the class. Students
volunteered to go to the board
to do whatever
work they knew how to do
and wished to contribute.

Specific techniques and
common fraction patterns
were emphasized.

HOMEWORK
DUE MONDAY
12/14/2009

NO SPECIFIC ASSIGNMENT DUE
BUT...

THERE IS A TEST WEDNESDAY 12/16/2009
ON TRIG FUNDAMENTAL IDENTITIES.

[PERIOD 6 STUDENTS who wish to work out
the last identity proof problem on Friday's Quiz (12/11/2009)
may go to www.hotmath.com USE PASSWORD

Once on hotmath.com, select Green Text (Stewart),
select page 472, select problem 41.
Now YOUR problem is actually problem number 42,
but problem 41 is worked out at www.hotmath.com,
and it is very, very similar to your problem.]

CLASS ACTIVITY
FOR MONDAY
12/`14/2009

The class is given 9 problems written on the whiteboard.
Students are to prove that each is an IDENTITY
using the Fundamental Identities from Trig.

As each problem is worked. (or as difficulty develops
with each problem) students can receive a copy of
a handout sheet where THAT SPECIFIC problem is worked completely.

Students can work together or alone to develop
their proofs. The teacher is available should students
arrive at a point that they cannot work
further on their own.

The board problems are actually the following problems
found in your GREEN TEXT BOOK, PAGE 471,
PROBLEMS 37, 38, 39, 41, 42, 43, 44, 45, & 46
Students can use www.hotmath.com and their school
ID to develop proofs in ODD PROBLEMS..

HOMEWORK
DUE FRIDAY 12/11/2009

BLUE TEXT PAGE 131 problems 11 through 19.
GREEN TEXT PAGE 472 problems 55 and 69.
(Students can use www.hotmath.com with GREEN text only.)

NOTE THAT WE WILL BE TAKING A TEST
ON PROVING TRIG IDENTITIES
ON TUESDAY OF NEXT WEEK.
THIS TEST WILL BE CRUCIAL TO YOUR
3rd QUARTERLY GRADE REPORT THAT
WILL BE POSTED ON DECEMBER 18, 2009.

GET CAUGHT UP... DO THIS AND ALL HOMEWORK.

CLASS ACTIVITY
FOR FRIDAY
12/11/2009

TOOK A POP QUIZ
to inform each student of
his/her proficiency in
understanding & proving
trig identities.

Worked problem 18, Blue Text p131.

Worked problem 55, Green Text p472

HOMEWORK DUE
THURSDAY 12/10/2009

DO PROOF PROBLEMS
10 through 19 FOUND ON
BLUE TEXT PAGE 131
(HANDOUT also AVAILABLE)

CLASS ACTIVITY
FOR THURSDAY 12/10/2009

USED COMPUTER WEBSITE
WWW.HOTMATH.COM AND
THE HOLLYWOOD ID
TO WORK PROBLEM 53 ON
PAGE 472 OF OUR GREEN
PRECALCULUS TEXT
BY STEWART (4 edition)

THIS PROBLEM ILLUSTRATED
ANOTHER TECHNIQUE FOR
PROVING IDENTITIES:


"MULTIPLY your problem
(or part of that problem) by
the CONJUGATE of one of
the denominators."

We will practice working
problems from the Stewart
text, where students can
use assistance from the
www.hotmath.com website.

HOMEWORK DUE
WEDNESDAY 12/09/2009

COMPLETE AND HAND IN
IDENTITY PROOF
PROBLEMS 6 through 10
BLUE BOOK PAGE 131
(COURTESY HANDOUT).
IF YOU DID NOT COMPLETE THEM
ALL IN CLASS ON TUESDAY.

CLASS ACTIVITY
FOR WEDNESDAY
12/09/2009

DO PROOF PROBLEMS
11 through 19 FOUND ON
PAGE 131 OF BLUE TEXT.
[THE CLASS MAY REQUIRE AN
ADDITIONAL DAY ON THIS ASSIGNMENT.]


For the first time it appears that
many students can prepare proofs
using trig identities. Each given
equation is different, and each requires
unique analysis. We are using
some 18 Fundamental Trig Identities
for our proofs to this point. We will acquire
and add to our list SEVERAL MORE
IDENTITIES...

HOMEWORK FOR
TUESDAY 12/08/2009

DO PROOF PROBLEMS 1 through 5
BLUE TEXT PAGE 131
IF YOU DID NOT COMPLETE THEM
ALL IN CLASS TIME.

CLASS EXPERIENCE
FOR SHORTENED DAY PD
TUESDAY 12/08/2009

Class works together Identity Proof #7
Blue Book Page 131 (courtesy worksheet)
on whiteboard.

DO IDENTITY PROOFS 6 through 10
Blue Book Page 131
to be turned in end of class.

HOMEWORK FOR
MONDAY 12/07/2009

COMPLETE UNFINISHED PROBLEMS
FROM BLUE TEXT PAGE 127
PROBLEMS 8 through 27.

CLASS ACTIVITY FOR
MONDAY 12/07/2009

DO PROBLEMS 1 through 5
Blue Text page 131.

BEFORE DOING CLASSWORK
PROBLEMS, work Example 2
Blue Text page 129
on whiteboard with whole class.

[Point out to students that three
identities-- as well as the basic
pattern of Basic Math to find
common denominators and
add/subtract fractions-- are required to develop
the proof.]

THREE OF THE FUNDAMENTAL IDENTITIES:

csc(THETA) = 1/sin(THETA)

(sin(THETA))^2 = 1 - (cos(THETA))^2

tan(THETA) = sin(THETA) / cos(THETA)

HOMEWORK FOR
FRIDAY 12/04/2009

FINISH ALL PROBLEMS FOUND
ON BLUE TEXT PAGE 127.

The object is to develop skill in
proving trig identities.

Your effort and perseverance is
indispensable.

CLASS EXPERIENCE
FOR FRIDAY 12/04/2009

HAND IN COMPLETED PROBLEMS
FROM PAGE 127.

The class is working together on the board
whatever problems are left to be done
on Blue Text page 127 9 through 27.
Students copy problems as they are
worked out.

Objective: to develop the skills to prove
trig identities using the Fundamental
Identities and techniques of algebra:

[convert to sines & cosines where
useful; use basic math patterns for
adding & multiplying fractions; multiply
by conjugates where useful, etc.]

HOMEWORK FOR
THURSDAY 12/03/2009

Students acquire a better understanding
of how to analyze and respond to
Identity Problems with each day's
practice & class discussion.

GO BACK TO HOMEWORK
FOR Wednesday, 12/02/2009
AND WORK WHAT YOU COULD NOT
DO...

BE PREPARED TO DISCUSS THESE
PROBLEMS ON THURSDAY 12/03/2009.

CLASSWORK ACTIVITY
FOR THURSDAY 12/03/2009

We worked problems 7 & 8 from blue text page 127.
These two problems were a part of assigned homework.

Additional effort went into identifying suitable
replacements for parts of trig expressions that
were to be proved or changed in form.

(a) Two corollaries to the The Pythagorean Theorem
were provided:

"Sine-squared THETA equals 1 minus Cosine-squared THETA."

"Cosine-squared THETA equals 1 minus Sine-squared THETA."


(b) Forms of basic fraction addition & multiplication were
examined and emphasized as the patterns for how to
manipulate trig-expressions.

COMPLETION OF ALL PROBLEMS ON PAGE 127 IS
THE OBJECTIVE, BUT that completion eludes us because we need
further development in the whole array of basic math, algebra, and
trig facts to do them. Please persevere... It's the only way...

HOMEWORK FOR
TUESDAY 12/02/2009

DO BLUE TEXT
PAGE 127 (Handout)
PROOF PROBLEMS 6, 7, & 8

THEN ATTEMPT
BLUE TEXT PAGE 127 (Handout)
problems 11, 12, & 13

[These problems ask that
you change whatever expression
is given to you into another that uses
only SINE trig functions-- of course
this is the opportunity to replace
parts of the given problem with
other EQUALLY TRUE statements
that have in them only SIN x.].

CLASS EXPERIENCE FOR
WEDNESDAY 12/02/2009

(1) QUIZ: WRITE FROM MEMORY
ALL TRIG DEFINITIONS, FACTS
AND IDENTITIES THAT WE HAVE
STUDIED SO FAR:

Use this outline:

I. Write Definitions of the six Trig Functions.
(To help you, make a diagram of angle THETA
in Standard Position. Draw its Reference
Triangle with sides labeled y, x, and r.)

1. ___________ 6. _____________
2. ___________ 5. _____________
3. ___________ 4. _____________

II. Write the six Reciprocal Identities.

7.__________ 12. _____________
8. __________ 11. _____________
9. __________ 10, _____________

IV, Write the two Ratio Identities.

13. __________ 14. ____________

V. Write the Pythagorean Theorem
in four forms:

15. (Use x, y, and r)
16. (Use sin# and cos#)
17. (Use tan# and sec#)
18. (Use cot# and csc#)

STUDENTS NEED TO KNOW THESE
FUNDAMENTAL FACTS & IDENTITIES
BY MEMORY...

(2) Go over homework problem 5 in class.

(3) Work homework problem 11 in class.
(This problem was not completed entirely
in class; so it will be done again in class
on Thursday, 12/03/2009.)

IT IS EXTREMELY IMPORTANT TO
ATTEMPT PROBLEMS 11, 12, & 13 ON
TEXT PAGE 127 UNTIL YOU CAN
WORK THEM CORRECTLY.

HOMEWORK
TO BE HANDED IN
TUESDAY 12/01/2009

DO PROOFS OF IDENTITIES 4 THROUGH 10
IN BLUE TEXT ON PAGE 127

CLASSWORK FOR
TUESDAY 12/01/2009

CONTENT OR CLASS ACTIVITY

(1) Work homework problems 4 & 5
from last night. Continue
demonstration of how to create the
proof of some given equation of
trig functions, building on KNOWN TRUE
IDEAS/STATEMENTS.

(2) Emphasize developing a
personal archive of TRUE statements
(like basic trig definitions) (the
pythagorean theorem-- algebraic AND
trig forms) that a student can use
to create their proofs.

(3) Call attention to the locations where
one TRUE FACT will be substituted
into SOME OTHER TRUE FACT to
produce yet a another NEW TRUE
FACT.

(4) Call on everyone to
memorize the basic trig
definitions and trig facts
and identities for their use
as our study of IDENTITIES
continues.

PLEASE NOTE HOMEWORK...

CLASS EXPERIENCE ON
MONDAY 11/30/2009

DO & HAND IN AT END OF PERIOD:
PROOFS 2 & 3 in Blue Text on page 127

New Understanding (called "proving" identities)
is developed EMPLOYING the trig facts from all prior
lessons.

PROOF begins with a statement
that is known to be TRUE.

One then goes out into
the "universe" of their mind
gathering up ANY OTHER TRUE
STATEMENT that could be used to
replace a portion of the beginning
(or initial) known true statement.

The new form that occurs as
a result of substitution must be TRUE
because it was fabricated from
two statements, BOTH OF WHICH
WERE TRUE to begin with.

This process is repeated until
one arrives at a form of the
TRUE statement that is desired.

Sometime, novel algebraic or
trig truths are used. Practice
synthesizing proofs is the only
way to develop one's skill in
proving trig identities

READ BLUE TEXT PAGES 123-126
especially Example 2 to help with homework.

HOMEWORK DUE
WEDNESDAY 11/25/2009

Complete the 4 graphs started in
class for tan, cot, csc, & sec.

CLASS EXPERIENCE FOR
WEDNESDAY 11/25/2009

ALL THREE PAGES OF CLASSWORK GRAPHING
(FROM MONDAY & TUESDAY) WILL
BE HANDED IN TODAY. (tan, cot, sec, csc.)


PROBLEMS 1 through 9 OF THE
FINAL CUMULATIVE REVIEW
WERE BEGUN.
("Little blue book" p 349; OR
separate handout copies are available.)

These problems are to be worked
over the holiday; they are especially useful for students
who wish to improve their grades.

HOMEWORK FOR TUESDAY
11/24/2009

Complete whatever part of the
classwork that you did not do
in Monday's class. (DO NOT
LOSE PAPERS...)

The graphs can be generated more quickly
on Tuesday if each student is "caught up"
before arriving in class.

Come in after school for questions
if needed.

CLASS EXPERIENCE FOR
TUESDAY 11/24/2009

PRODUCE ONE SHEET CONTAINING
THE 4 GRAPHS DESCRIBED BELOW.
(Save the paper to be turned in
Wednesday 11/25/2009 along with
the two papers generated
Monday 11/23/2009.)

Use a graphing calculator to produce
graphs that you will copy onto coordinate paper

(USE 4 DIFFERENT COORDINATE SYSTEMS
FOR THE GRAPHS BELOW.)

(1) GRAPH ONE y = tan(x)

(2) GRAPH TWO y = cot(x)

(3) GRAPH THREE y = csc(x) & y = sin(x)
on the same coordinate system.

(4) GRAPH FOUR: Y = sec(x) & y = cos(x)
on the same coordinate systems.

HOMEWORK FOR MONDAY
11/23/2009

Read text pages 419 and 420 S-L-O-W-L-Y!!!!!!!
(One cannot speed read math like a novel or a news paper.)

In the short week approaching, we will learn to
graph the tangent and cotangent functions.

CLASS EXPERIENCE
FOR MONDAY 11/23/2009

OBJECTIVE: to learn how to graph
y = tan (x) , y = cot (x) , y = csc (x) ,& y = sec(x)

TODAY:
Do without looking in text. Then compare your results with text. Work as a whole class.

(1) Create a table of values for x & y = tan (x)
using intervals along the x-axis of:
-60-deg; -45-deg; -30-deg ; 0-deg ;
+30-deg ; +45-deg ; and +60-deg.

(SEE Table 8 on text page 419)

(2) FOR YOUR COORDINATE SYSTEM USE SCALE:
12 horizontal boxes represents PI units.
4 vertical boxes represents ONE unit.
(Mark horizontal x-axis with points for
-PI/3 ; -PI/4 ; -PI/6 ; 0 ;+ PI/6 ; +PI/4 ; +PI/3)


(3) Then graph on the coordinate system drawn in step (2)-above
the ordered pairs (x, y) formed in step (1) above.

A graph of ONE PERIOD
of the function y = tan (x)
is generated by these 3-steps.

SAVE ALL PAPERWORK & GRAPH PAPER TO
CONTINUE THIS TOPIC TOMORROW.

TEST ON GRAPHING
on Friday 11/20/2009

(See previous class and homework assignments
on trig graphing... Invariably, all prior trig knowledge
is drawn upon in any trig test...)

CLASS EXPERIENCE
THURSDAY 11/19/2009

DO PROBLEMS AS FOLLOWS found on text pg. 416.
58 and 60 (Match graph to the given function.)
61 through 64 (Draw graphs from scratch.)
71 through 74 (Given values A & B, write function equations.)
75 and 76 (Look at the picture/graph, write a function for it.)
TWELVE PROBLEMS IN TOTAL...

HAND IN COMPLETED PROBLEMS AT END OF THE PERIOD.
We reviewed basic shape of sine & cosine functions; we recalled
the meaning of A & B; we used B-value to calculate Period by formula: P = (2PI)/|B|

HOMEWORK
FOR WEDNESDAY WEDNESDAY WEDNESDAY
11/18/2009
Text page 414 problems 9 & 11
Text page 415 problems 21, 24, 25, 27, 29, 31, 34, & 35
***********************************************************************
Students can bring questions to class Tuesday 11/17/2009.
Students may refer to more explanations
and examples in the text as follows:

Displacement on page 405 Example 1
Amplitude on page 408 Line of RED 3
Period on page 408 Line of RED 3
FORMULAS are found in yellow shaded box on bottom of page 489.
********************************************************************
You might try problems 10 & 13 first on this Yahoo tutorial page.
Click "Chapter 6: Graphs of Trigonometric Functions" when you get there...
YAHOO TUTOR
HERE-->

CLASSWORK
Text page 416 problems 47 through 56.
(Match with figures A through J on pages 415 and 416.)
HAND IN AT END OF THE PERIOD.

Content: Given assorted sine and cosine equations with varying A & B values,
determine the graphs of each function & match equations with graphs provided.
We worked two such problems in class before beginning exercises.

CLASS EXPERIENCE ON
TUESDAY 11/17/2009

Worked problems found in last night's homework
WHICH ARE DUE TOMORROW...

Discussed the parameters helpful in graphing the function y = A sin B(x) + D

Both yesterday's and today's experience is intended
to develop student's ability to graph the trig function
y = A sin B( x - C) + D

HOMEWORK FOR
MONDAY 11/16/2009

DO Text p 415
problems 13, 15, & 17

(Answers available from
class conversation &
your notes; OR read
figure 50 text page 403.)

OPTIONAL: DO text p 415
problem 14.
(See figure 55 text page 405
for graph of y = cos(x). )

CLASS EXPERIENCE:
MONDAY, 11/16/2009

AT THE CLOSE OF CLASS TODAY:
EVERY STUDENT WILL HAVE A PAGE
OF THE GRAPHS OF VARIOUS SINE FUNCTIONS.[8 items]

We are developing methods for graphing the general sine function:
y = A sin B(x - C) + D

Define & explain A ( |A| gives Amplitude of the graph...)
Define & explain B (Use |B| to calculate the Period of the function...)
Define & explain f (Frequency: which is related to Period. See formula definition)
Define & explain D (Displacement of the graph vertically.)

Later in the week, we will explore the parameter C, which is called Phase Shift,
the effects of which are to move the graph either right or left on the x-axis.]

READING DUE 11/13/2009
Read text p402 (yellow box)
Read text p403 item "1"
"GRAPH TRANSFORMATIONS OF THE SINE FUNCTION"
Look at figures 49 & 50
Read text p404
"PROPERTIES OF THE SINE FUNCTION" ( 1 through 6)

IN CLASS WE FINISHED GENERATING THE GRAPH
OF y = sin (x) TOGETHER.

WE MADE A TABLE OF x and y values
in increments of 30-degrees from 0-deg
through 360-deg. Then we plotted each
ordered pair...

WE WENT THROUGH
(and discussed) THE LIST
OF 6 CHARACTERISTICS
OF y = sin(x) found on text page 404.
(yellow shaded area)

HOMEWORK DUE THURSDAY 11/12/2009

Worksheet that illustrates how to compute
Angular Displacement in Radians (called THETA)
AND Angular Velocity (OMEGA)

Problems 1-6
(Refer to text page 365 to see similar problems worked out)

WORK IN PROGRESS:
BEGIN THE GRAPH OF y = sin (x)
AS A WHOLE CLASS...
You are supplied special graph containing unit circle
and horizontal scale 12 horizontal units = PI.

We will complete the graph of y = sin (x) and y = cos (x) tomorrow.

HOMEWORK:
For: Tuesday, 11/10/2009

Finish Applications Problems
that demonstrate ANGULAR VELOCITY
CALCULATIONS: text page 368 problems 97 & 98
(Extra Credit problem 100)

CLASSWORK: 11/09/2009
Continue study of velocities: LINEAR and ANGULAR.

Warm-up: basic velocity problems using only formulas. (No applications.)

Applications: text p368: prob 97(angular velocity);
prob 98 (both linear velocity & angular velocity).

FOR FRIDAY 11/06/2009

PUT HOMEWORK PAPERS
IN THE FOLDER FOR THIS PERIOD.
DO text pg 368 problems 104, 106, and 108.

Use the linear velocity formula v = s/t
and the angular velocity formula OMEGA = (THETA)/t

11/06/2009 Friday

HAND IN ALL CLASSWORK PAPERS AT END OF PERIOD.
PLACE THEM IN THE FOLDER FOR THE PERIOD.

DO text p 370. Exercises 117, 118, 119, 120, and 121.
Copy the questions.
Make complete statements to answer the problems,
and include formulas & diagrams where useful.

No written homework for Thursday 11/05/2009
Read page 365:
Linear Speed (in Linear Motion: as in miles/hour or feet/second)
Angular Speed (in Circular Motion: as in radians/second; revolutions/minute)

TEST: See Topic Review sheets 1 thru 3 from (11/03/2009)

PRACTICE TEST: topics for tomorrow's test.:
a. How to draw an angle in Standard Position:
(1) where is the initial side?
(2) where is the terminal side?
(3) clockwise vs counter-clockwise rotation causes neg & pos angles
(4) all angles lie in one of 4 quadrants. know which quadrant an angle is in.
(5) know the 3 systems of angle measurement;
(i) degrees: Decimal degrees
(ii) degrees: Deg Min Sec
(iii) Radians
(6) know how to convert from one measuring system to another
(7) know formula definition of an angle measured in radians :
THETA = (ARC LENGTH)/RADIUS
(8) know formula to calculate arc length:
ARC LENGTH = RADIUS * THETA
(9) know formula to calculate area of a sector:
SECTOR AREA = 1/2 *(RADIUS)^2 * THETA

text p367: odd 71 thru 77 and all 87 thru 90

Page 274 1-51 odd