Introduction to the course and discussion of course policies.
In-Class Activity: Oh Deer!
For Wednesday, August 27
Read: Sections 6.1 and 6.2 (and 4.1/4.2 Review)
Review: Section 4.1 -- 7, 15, 16, 20 and 4.2 -- 22, 23
Graphed the height of a Ferris Wheel car as a function of time, reported midline, amplitude, period of a sinusoidal function.
For Tuesday, January 22
Read: Section 6.3
Review: Section 6.1 -- 1, 5, 7, 9, 13, 15, 17, and 18
Defined the sine and cosine of an angle.
Read:
Section 6.3
Do: Section 6.2 -- 1, 3, 7, 9, 11, 16, 17, 18
Quiz 1 on Wednesday over Review (4.1/4.2) and Section 6.1
Took Quiz 1.
Defined the radian measure of an angle and did some work with arc length.
Read: Section 7.1 (brief jump)
Do: 6.3 -- 1 through 8, 12, 15, 17, 19, 23, 24
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.
Read: Section 6.4 and 6.5
Do: Worksheet on finding the angle (Here's the key.) and Internet assignment (e-grade) for Wed. Sept. 10. You MUST register first here and make your own password.
Got familiar with SOHCAHTOA.
Read: Section 6.4 and 6.5
Do: Section 7.1 -- 1-4, 6-8, 12, 17, 18 and Internet Assignments (e-grade) You MUST register first here and make your own password. HW 1 is over selected topics in Chapter 6 and due 11:59 PM Wednesday September 10.
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:
- 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.) - 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.)
Due for Friday, September 12
Read: Section 5.4 (to look at horizontal stretching) and 6.5
Do: Section 6.4 -- 1-12, 14, 15, 18 and prepare for QUIZ 2 on
6.2, 6.3, worksheet on angles, and 7.1
We explored the effects of B and h on the graph.
Due for Monday, September 15:
Read: Section 6.6 and 6.7
Do: Section 6.5 -- 5, 7, 12 through 28, 35, 49
After taking the quiz, we investigated the tangent function and its properties.
Due for Wednesday, September 17:
Read: Section 6.7
Do: E-Grade HW 2 due 11:59 PM Wed, Sept 17 and be prepared for QUIZ 3 on 6.4 and 6.5
Test 2 is on Monday Sept 22.
Looked at other trig functions, namely secant, cosecant, and cotangent.
Due for Friday, September 19:
Read: Section 6.7 and 7.1 (again)
Do: Section 6.6 -- 1 through 16, 23-25, 27
Reviewed for Test 1 over 4.1, 4.2, 6.1-6.6, 7.1
Took Test 1
We explored a group activity called Watch the Birdie. Similar problems are on the handout.
Read: Section 6.7 again and Section 7.2
Do: Section 6.7 -- 1, 21-24, 26, 30 and Section 7.1 -- 5, 10, 11, 13 and handout.
Read: Section 7.2
Do: Section 6.7 -- 1-16, 24, 25, 30 and Section 7.2 -- 1, 3
Law of Cosines
Read: Section 7.3
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 and Key to Page 2. Also be prepared for QUIZ 4 over 6.7, worksheet., 7.1, and 7.2 (Law of Sines)
After taking Quiz 4, 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).
Check the 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 7.4 and 7.6
Do: Section 7.3 -- 3, 13, 14, 17, 23, 25, 28, 30b and Section 6.7
#25 and Chapter 6 Review 23 - 30
For Wednesday: practice with Identities and Equations (includes key).
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.
Polar coordinates
Read: Section 8.1 and 8.2
Do: Section 7.6 -- 1-7, 12-18 and be prepared for a QUIZ 5 on 7.2 and 7.3
Composition of Functions
Read: Section 8.2
Do: Section 8.1 -- 10-25, 33-44
HW 3 eGrade due 11:59 PM Friday October 17
| Monday, October 13 Fall Break |
|
Photo by Kathy Hanby. Used with permission.
Decomposition of Functions, Inverses
Read: Section 10.1 (Skipping 8.3)
Do: Section 8.1 -- 53-59 and Section 8.2 1-13 odd, 19, 21, 51, 63 and Chapter 8 Review 41-53.
Be prepared for QUIZ 5 over 7.4, 7.6, and 8.1
HW 3 eGrade due 11:59 PM Friday October 17
Vectors. Here's a handout we worked on that was a page from old exam.
Read: Section 10.2
Do: Section 10.1 -- 11, 12
Be prepared for QUIZ 6 over 8.2
HW 3 eGrade due 11:59 PM Friday October 17
HW 4 eGrade due 11:59 PM Wednesday October 22
TEST 2 over 6.7, 7.1, 7.2, 7.3, 7.4, 7.6, 8.1, 8.2 and 10.1 on Friday, October 24
For Friday: TEST 2 over 6.7, 7.1, 7.2, 7.3, 7.4, 7.6, 8.1, 8.2 and 10.1 on Friday, October 24
IMPORTANT: No formulas provided, but you are allowed to bring one sheet of 8.5 by 11 inch paper on which you wrote anything you want that you feel would be useful. Must be in your own handwriting. One side of the paper, please. If you skipped class today, I hope you remembered to look at this!
QUIZ 7
TEST 2
Vectors. Looked at Section 10.2 # 15, then Chapter 10 Review # 3. Also found the lengths of the 3-D vectors.
Read: Section 10.3
Do: Section 10.2 1-24 and Chapter 10 Review 1-4
Wrote the 3D vectors below in component form and found their lengths
Looked at operations with revenue vectors and an application problem involving Broom Hilda and a nasty wind.
Read: Section 10.4
Do: Section 10.3 1, 4, 5 and Chapter 10 Review 5
Dot product! Found the angle between a and b in the figure above.
Read: Section 11.1
Do: Section 10.4 1-6, 8-10, 17, 19 and a QUIZ 8 on 10.2 and 10.3
Sequences
Read: Section 11.2
Do: Section 11.1 1-5
Sequences
Read: Section 11.3
Do: Section 11.1 1-5, 7-11, 15, 16, 18 and Section 11.2 1-8, 11-16, 19, 20, 23, 24
HW 5 eGrade over topics in Chapter 10 due 11:59 PM Wednesday November 12
Series, Partial Sums
Read: Section 11.3
Do: Prepare for QUIZ 9 over Section 10.4 and 11.1
HW 5 eGrade over topics in Chapter 10 due 11:59 PM Wednesday November 12
Infinite Series
Read: Section 11.3
Do: Section 11.2 1-25 odd, 33 and this Worksheet on Ritalin.
Parametric Equations
Read: Section 11.4
Do: Section 11.3 -- 1, 5, 6, 10, 13, 15, 18, 19, 24, 25, 26, 28 and QUIZ 10 on 11.1 and 11.2
HW 5 eGrade over topics in Chapter 10 due 11:59 PM tonight
HW 6 eGrade over topics in Chapter 11 due 11:59 PM Sunday November 16
Circles and Ellipses
Read: Section 11.4 on Hyperbolas
Do: Section 11.4 -- 1a, 2a, 9, 13, 15, 17, 18, 20-22
Hyperbolas
Do: Section 11.4 -- 3a, 11, 13 and QUIZ 11 on 11.3 and 11.4
Read: Section 11.5
Do: Section 11.4 -- 4 through 8 (just identify the conic section), 11, 12
Name that conic, Complex numbers
Read: Section 11.5
Do: Section 11.5 -- 7-11
Read: Section 11.5
Do: Prepare for Test 3 over Chapter 10 and Sections 11.1-11.4
Holiday Bonus: All past eGrade assignments may be redone by 11:59 Tuesday, Dec. 9
Do: Section 11.5 -- 1-21 odd
The last quiz over complex numbers is Monday.
The Final Exam will be Monday, Dec. 15, 2003 1:00- 3:00 pm
Here's the Review for the Final.