MA 154 Spring 2003

Syllabus

Important Notices, Handouts, and Assignments
NOTE: Some of the links below will be handouts that can be viewed and printed with your web browser. Others will be PDF documents that must be read with Adobe™ Acrobat™ Reader software. This software is free and available from Adobe's Web Site. 
Tuesday, January 14: Welcome to MA 154!

Introduction to the course and discussion of course policies. 
In-Class Activity: Oh Deer! 

For Thursday, January 16
Read: Sections 6.1 and 6.2
Review: Section 4.1 -- 7, 15, 16, 20 and 4.2 -- 22, 23
Thursday, January 16: Periodic Functions, Sine and Cosine
Graphed the height of a Ferris Wheel car as a function of time, reported midline, amplitude, period of a sinusoidal function. Defined the sine and cosine of an angle..
For Tuesday, January 22
Read: Section 6.3
Review: Section 6.1 -- 1, 5, 7, 9, 13, 15, 17, and 18 and 6.2 -- 1, 3, 7, 9, 16, 17
Tuesday, January 21: Radians
 Defined the radian measure of an angle and did some work with arc length.
 Due for Thursday, January 13
Read: Section 7.1 (brief jump)
Do: Section 6.2 -- 11, 18 and 6.3 -- 1 through 8, 12, 15, 17, 19, 23, 24
Quiz 1 on Thursday over Review (4.1/4.2) and Sections 6.1 and 6.2
Thursday, January 23: Section 7.1
Took Quiz 1
Looked at exact values (see activity) of trig functions of 30Ί, 45Ί, 60Ί and their multiples, did some problems from the worksheet on finding angles in radians (exactly), and looked at right triangle definitions and applications. 
 Due for Tuesday, January 28
Read: Section 6.4 and 6.5 
Do: Section 7.1 -- 1-4, 6-8, 12, 17, 18 and worksheet on finding the angle (Here's the key.)
Remember Test 1 is next Thursday
Tuesday, January 28: Review and Section 6.4
Reviewed for the exam. It will cover 4.1, 4.2, 6.1, 6.2, 6.3, 7.1 and some of 6.4. Here's a review sheet that tells everything about it. 
We discussed the domain, range, period, and amplitude of y = sin(x) and y = cos(x) and how these can be determined from the unit circle. We looked at graphs of two forms:
  1. y = Asin(x) and y = Acos(x) have amplitude |A|. 
    For A > 0, 
    the graph of y = Asin(x) stretches or compresses the graph of  y = sin(x) by A units.
    the graph of y = –Asin(x) is a vertical reflection of the graph of y = Asin(x).
    Similarly for y = cos(x).  
    (See Section 5.2 and 5.3 for a review of these topics.)
  2. y = sin(x) + k and y = cos(x) + k have midline k.
    For k > 0, 
    the graph of y = sin(x) + k shifts the graph of y = sin(x) up k units.
    the graph of y = sin(x) – k shifts the graph of y = sin(x) down k units.
    Similarly for y = cos(x).  
    (See Section 5.1 for a review of these topics.)
The first multiplies the output by a quantity; the second adds/subtracts a quantity to the output. In the next class after the test we will look at the effect of doing both of these kind of transformations to the input.

Due for Tuesday, February 4
Read: Section 5.4 (to look at horizontal stretching) and 6.5 
Do: Section 6.4 -- 1-12, 14, 15, 18
Tuesday, February 4
One equation says it all: y = Asin(B(x - h)) + k
We explored the effects of  B and h on the graph.
 Due for Thursday, February 6:
Read: Section 6.6 and 6.7 
Do: Section 6.5 -- 5, 7, 12 through 20, 24, 28, 35, 49
Thursday, February 6:
After returning the tests, we investigated the tangent function and its properties.
Due for Tuesday, February 11: 
Read:  Section 6.7
Do:  Section 6.6 -- 1 through 15, 24, 25 and QUIZ 2 on 6.4 and 6.5
Tuesday, February 11: 
After the quiz, we discussed Section 6.6 and section 6.7
Due for Tuesday, February 13: 
Read:  Section 7.1 (re-read again) and 7.2
Do:  Section 6.6 -- 14, 15, 16, 30 and Section 6.7 -- 1-19 as needed 
(Hint for 19: ) and Section 7.1 -- 5, 9, 11.
Thursday, February 13:
After returning the quiz and discussing the homework, we talked about finding the angle if given two of the sides using the inverse trig functions. We explored a group activity called Watch the Birdie. Similar problems are on the handout.
Due for Tuesday, February 18: 
Read:  Section 7.2
Do:  Chapter 6 Review-- 23-30, 43, 49, 50, 51, 54 and handout. 
Be prepared for QUIZ 3 on 6.6, 6.7, and finding angles as done in 7.1 --5, 9, 11
Tuesday, February 18:
Law of Sines
Due for Thursday, February 20: 
Read:  Section 7.2
Do:  Section 7.2 -- 1, 3, 4, 5, 17, 21, and 23
Thursday, February 20 
Law of Cosines
Due for Tuesday, February 25: 
Read: Section 7.3 & 7.4
Section 7.2 -- 2, 6, 7, 8 through 13, 15, 16, 19, 20, 22, 24, 27 and Law of Sines and Cosines to the Rescue handout  (Page 1, Page 2). Here is the Key to Page 1 (corrected) and Key to Page 2.  Also be prepared for QUIZ 4 over 7.2 (Law of Sines) and 6.7 (Watch the Birdie)
 Also, the first Internet assignment is due Thursday, Feb 27. Here are the  directions.
Tuesday, February 25
After taking Quiz 4 (here's its KEY), we looked at identities and why they can be useful in solving an equation like cos2x + 4sin x = 4 for x in [0, 2pi).
Once you substitute 1 – sin2x for cos2x, you have an equation only involving the same trig function: 

cos2x + 4sin x = 4
1 – sin2x + 4sin x = 4

The rest is algebra.... 

1 – sin2x + 4sin x = 4
–sin2x + 4sin x = 3
–sin2x + 4sin x – 3 = 0
sin2x – 4sin x + 3 = 0
(sin x – 3)((sin x – 1) = 0
sin x = 3 and sin x = 1
sin x = 3 has no solutions and sin x = 1 has a solution of pi/2.

How nice! After introducing the double angle formulas, similar fun was done for solving cos 2x = cos x on  [0, 2pi).
Replace cos 2x with 2cos2x – 1 and turn the crank....

cos 2x = cos x
2cos2x – 1 = cos x
2cos2x –  cos x – 1 = 0
(2cos x +  1)(cos x – 1) = 0
cos x = –1/2 and cos x = 1
x = 2pi/3, 4pi/3 and x = 0

Note that 2pi is a solution but not in the requested interval of  [0, 2pi).
We checked our solution by graphing y = cos 2x  – cos x and watching it touch the x-axis at the three values 0, 2pi/3, 4pi/3. 
It was handy to set Xscl = pi/3. You could also have graphed y = cos 2x and y = cos x and see when they intersect.

Read: Section 7.6
Do: Section 7.3 -- 3, 13, 14, 17, 23, 25, 28, 30b and Wilbur handout and KEY
Thursday, February 27:
 We provided some review problems which may help doing the Internet assignment.
We talked more about finding solutions, and what to do if we want ALL solutions, rather than just those in a restricted interval.
One approach is to simply find the those in the interval of  [0, 2pi) and add "2pi*k, where k is an integer" to those that were found.
We worked on the handouts below, honing our appreciation of the inverse trig functions as angles.
Read: Section 7.4 (We're skipping 7.5)
Do:  practice with Identities and Equations (includes key). (Skip 4c and 5 until after 7.4)
The Internet (e-grade) assignment is due tonight by 11:00 pm. 

Note that our next exam in one week from today covering sections 6.4, 6.5, 6.6, 6.7, 7.1, 7.2, and 7.3.
Need some help practicing Section 6.4 and 6.5? Try e-grade and select the Tutorial or Quiz for Graphs of Trigonometric Functions.
Tuesday, March 4: Sum and Difference Identities, Polar Coordinates, Composition of Functions
Here is a review for the test on Thursday.

In some texts, there is a TYPO on page 306. Check that the formula is the same as that in the box on page 308.  We looked at  Sum and Difference Identities handout and KEY.  We skipped the second page.
We converted from rectangular coordinates to polar coordinates and vice versa.
Spent a little time looking at Section 8.1
Due March 24: e-grade Internet Assignments 2 and 3 on Polar Coordinates and Function Composition
Due March 18: Section 7.6 --1-8 and Section 8.1 --10-25, 33-44.
Tuesday, March 18:
One approach is to simply find the those in the interval of  [0, 2pi) and add "2pi*k, where k is an integer" to those that were found.
We worked on the handouts below, honing our appreciation of the inverse trig functions as angles.
Read: Section 10.1 (We're skipping 8.3)
Do: Section 8.2 --1-13 odd, 19, 21, 51, 63 and get cracking on those Internet assignments.
Thursday, March 20
Fun with vectors!
Read: Section 10.2 and 10.3 
Do: Section 10.1 -- 1 through 11 and Section 10.2 -- 1 through 5, 7 through 9, 15, 17 and prepare for QUIZ 5 on 7.4, 7.6, 8.1, and 8.2
Tuesday, March 25
More fun with vectors.
Read: Section 10.4  
Do: Section 10.2 -- 10 through 17 and Section 10.3 -- 1, 4, 5 and Chapter 10 Review -- 1 through 6, 18, 19, 21.
Thursday, March 27
Dot product!
Read: Section 11.1  
Do: Section 10.4 -- 1-6, 10 and prepare for QUIZ 6 on 10.1-10.3. Also do the two Internet (e-grade) assignments due April 3. Note: you can get your grades here.
Tuesday, April 1
After taking QUIZ 6 (Here's a KEY), we had fun with Section 11.1
Read: Section 11.2  
Do: Section 11.1 -- 1-5, 7-11, 15, 16, 18 and do the two Internet (e-grade) assignments.
Thursday, April 3
Section 11.2
Read: Section 11.3  
Do: Section 11.2 -- 1-8, 11-16, 19, 20, 23, 24, 33 and prepare for QUIZ 7 on 10.4 and 11.1
Tuesday, April 8
Section 11.3
Read: Section 11.4  
Do: Section 11.3 -- 1, 5, 6, 10, 13, 15, 18, 19, 24, 25, 26, 28
Thursday, April 10
Section 11.4
Read: Section 11.4  about hyperbolas
Do: Section 11.4 -- 1a, 2a, 9, 13, 15, 19, 20, 21 and prepare for QUIZ 8 on 11.2 and 11.3
Next Internet Assignment #4 (e-grade) on vectors (Section 10.4) due April 17.
Tuesday, April 15
Section 11.4
Read: Section 11.5  
Do: Section 11.4 -- 1b, 2, 3b, 4-8, 11, 12, 27 and Chapter 11 Review # 17 and prepare for QUIZ 9 on 11.4  (circles and ellipses)  
Next Internet Assignment #4 (e-grade) on vectors (Section 10.4) due April 17.
Thursday, April 17
Section 11.5
Do: Section 11.5 -- 7-11
Tuesday, April 22
Discussed quiz and reviewed for Test 3. See Review sheet. 
Do: Prepare for TEST 3 on Thursday, April 24 and QUIZ 10 over Section 11.5 on Tuesday April 29. Get all e-grade assignments in by midnight Tuesday, April 29.
Thursday, April 24
Test 3
Tuesday, April 29
Returned Test 3. Took QUIZ 10 on Section 11.5. 
Do: Section 11.5 -- 1-21 odd and prepare for QUIZ 11 over Section 11.5
Thursday, May 5
Took QUIZ 11.  
The Final Exam will be Tuesday, May 6, 2003  1:00- 3:00 pm, Kettler G50
Here's the Review for the Final.

© 2003 Indiana University-Purdue University Fort Wayne, all rights reserved
Last updated: May 5, 2003
URL: http://users.ipfw.edu/lamaster/ma154/s03ma154.htm
Contact: John LaMaster, Instructor, (260) 481-5430
Comment Form: John LaMaster, Mathematical Sciences