Tuesday, Jan. 8
Periodic Functions
Syllabus
Internet Resources (with a link to the General Course Information)
Practice Questions to Check Prerequisite Skills Needed for MA 15400
Due: Thursday, January 10
Read: General Course Information, the Syllabus, and Section 7.1 and 7.2
Do: If necessary, purchase a TI-83 Plus/TI-84 Plus or equivalent and purchase eHW access.
Note: access is good for one year.
Practice on eHW Flash Cards: 7.1 Periodic Functions.
Optional: Section 7.1 -- your choice of 1-17, 23-34 as needed.
Review Practice Questions to Check Prerequisite Skills Needed for MA 15400 and see these Worked out Solutions.
You should also be proficient in these skills needed for MA 15300.
Prepare for QUIZ 1 next Tuesday, Jan. 15 over prerequisite skills.
Due
Thursday, Jan. 17, 11:59 pm: E-HW 0
- Part 1: John's Syllabus and E-HW0 - Part 2: General Course
Information and Using eHW
Due Thursday, Jan. 17, 11:59 pm:
E-HW 01
Sections 7.1 - 7.2
The Sine Function
(and its Sidekick, Cosine)
Practice on eHW Flash Cards: 7.2 Use the definitions of sine and cosine and 7.2 Report the coordinates of a point on a circle of radius r given the angle
Optional: Section 7.2 -- 1-31, 33-35 and read Section 7.3.
Prepare for QUIZ 1 Tuesday, Jan. 15 over prerequisite skills.
Due
Thursday, Jan. 22, 11:59 pm (extended): E-HW 0
- Part 1: John's Syllabus and
E-HW 0 - Part 2: General Course
Information and Using eHW
E-HW 01
Sections 7.1 - 7.2
Due Tuesday, Jan. 22, 11:59 pm:
E-HW 02
Section 7.3
Took QUIZ 1 over prerequisites.
| Defined radian measurement.
Suppose the vertex of an angle θ is at the center of a circle
of radius r, and the angle spans an arc of length s.
The measure of the angle θ in radians is defined as
the ratio of the arc length, s, to the radius r (See
figure). It follows that an angle of 360° spans an arc length of the
circumference of the circle, s = 2πr,
so this angle has a radian measure of = s / r = 2πr
/ r = 2π. Consequently 180°
is equivalent to π radians, which is a handy conversion factor. We
looked at converting angles from degrees to radians and vice versa,
with and without a calculator. Finally, we looked at some applied
questions where we were asked to find the arc length if given the
angle (in degrees) and the radius. It is paramount to convert θ
from degrees to radians first before applying the relationship s
= r*θ, since this only holds if θ is in
radians. Read: Chapter 7 Skills Refresher Optional: Section 7.3 -- 1-56 as desired and read Chapter 7 Skills Refresher Practice on eHW Flash Cards: 7.3 Degrees <=> Radians 7.3 Radian Measure as Number of Radius Lengths Around a Circle 7.3 Find points on a circle using radian measure of quadrantals 7.3 Arc Length of a Sector |
|
E-HW 0 - Part 2: General Course Information and Using eHW
E-HW 01 Sections 7.1 - 7.2
Due Tuesday, Jan. 22, 11:59 pm: E-HW 02 Section 7.3
Due Thursday, Jan. 24 - Writing Assignment 1: Bug on a Square Track
We worked some problems from Writing Assignment 2 on finding angles in radians (exactly).
Due: Tuesday, Jan. 22
Practice on eHW Flash Cards: Chapter 7 Skills Refresher Properties of Special Triangles
Chapter 7 Skills Refresher Exact Values of Sine and Cosine
Optional: Skills Refresher for Chapter 7 -- 1 - 32 and read Section 7.4
Tuesday, Jan. 22: QUIZ 2 over 7.1 and 7.2
Due Tuesday, Jan. 22, 11:59 pm (extended): E-HW 0 - Part 1: John's Syllabus and
E-HW 0 - Part 2: General Course Information and Using eHW
E-HW 01 Sections 7.1 - 7.2
Due Tuesday, Jan. 22, 11:59 pm: E-HW 02 Section 7.3
Due Thurs., Jan. 24, 11:59 pm: E-HW 03 Chapter 7 Skills Refresher
Due Thurs., Jan. 24 - Writing Assignment 1: Bug on a Square Track
Due Tuesday, Jan. 29 - Writing Assignment 2: What's My Angle?
We looked at an outside change to the function, which results in the original function being transformed vertically (change to the output).
-
y = Asin(x) and y = Acos(x) have amplitude |A|.
For A > 0,
the graph of y = Asin(x) vertically 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 the same holds for y = cos(x).
(See Section 6.1 and 6.2 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 vertically shifts the graph of y = sin(x) up k units.
the graph of y = sin(x) − k vertically shifts the graph of y = sin(x) down k units.
Similarly the same holds for y = cos(x).
(See Section 2.4 for a review of these topics.)
The first multiplies the output by a quantity; the second
adds/subtracts a quantity to the output.
For the function y = Asinx + k
or y = Acosx + k
we explored the effects of A and k to find that
this graph has
an amplitude of |A|, and midline which is y = k.
Due: Thursday, Jan. 24
Optional:
Section 7.4 --
1-24,
26-30, 34-38 and Chapter 7 Review 14a, 14d, 19-24, 51, 52, 69-71
and read Section 7.5
Practice on eHW Flash Cards: 7.4 Period, Amplitude, Midline
E-HW 0 - Part 2: General Course Information and Using eHW
E-HW 01 Sections 7.1 - 7.2
Due tonight, Tuesday, Jan. 22, 11:59 pm: E-HW 02 Section 7.3
Due Thurs., Jan. 24, 11:59 pm: E-HW 03 Chapter 7 Skills Refresher
Due Thurs., Jan. 24 - Writing Assignment 1: Bug on a Square Track
Due Tuesday, Jan. 29 - Writing Assignment 2: What's My Angle?
The graph of
y = sin(Bx)
(Inside multiplicative change)
For the function y = AsinBx + k
or y = AcosBx + k
we explored the effects of B on the period to find that,
for positive values of B, this graph has
a period of 2π/B.
Due
tonight, Thurs., Jan. 24, 11:59 pm:
E-HW 03 Chapter 7 Skills Refresher
Due Tuesday, Jan. 29
Practice on eHW Flash Cards:
7.5 Find a Formula of a Sine or Cosine Function (No Phase Shift Needed)
7.5 Find a Formula of a Sine or Cosine Function (Ferris Wheel)
Optional:
Section 7.5 -- 1-12, 21-26 and read Section 7.5 and,
if needed, Sections 2.4, 6.1, 6.2
Tuesday, Jan. 29: QUIZ
3 over Section
7.3
and Chapter 7 Skills Refresher
Due Tuesday, Jan. 29
-
Writing Assignment 2: What's My Angle?
For positive values of
A, B, h, k, and φ
we explored the graph of
y = Asin(B(x − h)) + k or
y = Asin(Bx − φ) + k
where h is the
horizontal shift to the right and
where φ = Bh is the
phase shift to the right.
Continued Section 7.5. If given a graph, find the midline, period, amplitude, and the horizontal and phase shifts. When specifying horizontal and phase shift, include whether it is regular sine or cosine (or upside down versions of these), whether it is shifted left or right, and by how much.
Due Tuesday, Jan. 29
Practice on eHW Flash Cards: 7.5 Find Phase Shift
7.5 Find a Formula of a Sine or Cosine Function (Phase Shift Needed)
Optional: Section 7.5 -- 27-31, 37, 38, 44-50 and read Section 7.6 and, if needed, Sections 2.4, 6.1, 6.2
Due Tuesday, Feb. 5
- 11:59 pm: E-HW 03 Section 7.4 and 7.5
- Writing Assignment 3: Trig Graphs
but over an interval of [0, 2π],
then today marks a special point between the Winter Solstice and the Vernal Equinox
which roughly correspond to π/6,
or one twelfth of the period.
"Groundhog Day" and the European feast called "Candlemas" are other popular ways this moment is marked..
In tribute to "π/6 Day", the Purdue Fort Wayne campus has given all students the day off to celebrate
(despite what you have heard about some other reason like a winter storm).
To enjoy the festivities, find the amplitude, midline, and formula of this graph and
use it to determine today's number of daylight hours.
Adapted from Duration of Daylight Tables
Tuesday, Feb. 5: QUIZ 4 over Section 7.4 and 7.5
Due Tuesday, Feb. 5- 11:59 pm: E-HW 03 Section 7.4 and 7.5
- Writing Assignment 3: Trig Graphs
No class meeting, Thursday, Feb. 7. You can come to our classroom for a Review Session any time from 9:00 - 11:45 AM
Due Tuesday, Feb. 12
Practice on eHW Flash Cards: 7.6 Graph of y = AtanBx
Optional: Section 7.6 -- 1-20
Due Tuesday, Feb. 5 (tonight), 11:59 pm: E-HW 04 Section 7.4 and 7.5
Due Tuesday, Feb. 19, 11:59 pm: E-HW 05 Section 7.6 -7.8
Test 1 this week. See review sheet. This is in the folder Reviews for Exams on Blackboard.
(It closes at 8:00 pm)
Walk-in testing available.
You can take Test 1 in the Math Test Center (KT G18) Thurs., Feb. 7, 9:00 AM-7:00 PM
(It closes at 8:00 pm.)
(It closes at 4:30 pm.)
This is the last day to take the test.
Practice on eHW Flash Cards: 7.7 Find exact values of all six trig functions of any angle
7.8 Solve trig equations for the exact value of the angle WITHOUT a calculator
7.8 Solve trig equations for the exact value of the angle WITH a calculator
8.1 Use right triangle definitions if given two sides
8.1 Use right triangle definitions if given the angle and a sides
Optional: Section 7.7 -- 1-20 and Section 7.8 -- 1-33 and Section 8.1 -- 1-47 as desired
Due Tuesday, Feb. 19, 11:59 pm: E-HW 05 Section 7.6 -7.8
Due Thursday, Feb. 21, 11:59 pm: E-HW 06 Section 8.1
Writing Assignment 4: The Golden Arch due Tuesday, Feb. 26
Practice on eHW Flash Cards: 7.8 Given the slope, find the angle of inclination
8.1 Use right triangle definitions - applications
8.2 Use Law of Sines or Law of Cosines to Solve Triangles
Read: Section 8.1 and 8.2
Optional: Section 8.2 -- 1-5, 7, 8, 32 - 35, 37, 41
Due Tuesday, Feb. 19, 11:59 pm:
E-HW 05 Section 7.6 -7.8
Due Thursday, Feb. 21, 11:59 pm:
E-HW 06 Section 8.1
Due Tuesday, Feb. 26:
Writing Assignment 4: The Golden Arch
Tuesday, Feb. 19: QUIZ 5 over Section
7.6-7.8
Practice on eHW Flash Cards:
8.2 Use Law of Sines or Law of Cosines to Solve Triangles
8.2 Determine the number of triangles that are possible
8.2 The Ambiguous Case
Read: Section 8.3
Optional: Section 8.2 -- 6, 9-31,36,40, 42-44, 47, 48
Due tonight, Tuesday, Feb. 19, 11:59 pm: E-HW 05 Section 7.6 -7.8
Due Thursday, Feb. 21, 11:59 pm: E-HW 06 Section 8.1
Due Tuesday, Feb. 26, 11:59 pm: E-HW 07 Section 8.2
Due Tuesday, Feb. 26: Writing Assignment 4: The Golden Arch
Due Thursday, March 14: Writing Assignment 5: The Law of Sines and Cosines to the Rescue
Due: Tuesday,
Feb. 26
Read: Section 9.1 and 9.2
Optional: Section 8.3 -- 1-22 and Section 9.1 -- 1-30,
38, 39, 41 and 9.2 -- 9-12
Due tonight, Thursday, Feb. 21, 11:59 pm: E-HW 06 Section 8.1
Right Triangle Trigonometry
Due Tuesday, Feb. 26, 11:59 pm: E-HW 07 Section 8.2 Law of
Sines and Cosines
Due Thursday, Feb. 28, 11:59 pm: E-HW 08 Section 8.3 and 9.1
Due Tuesday, March 12, 11:59 pm: E-HW 09 Section 9.2
Identities
Due Tuesday, Feb. 26: Writing Assignment 4: The Golden
Arch
Due Tuesday, March 12: Writing Assignment 5: The Law of
Sines and Cosines to the Rescue
Optional: Section 9.2 -- 13, 15, 19 - 30, 55 - 58
Due tonight, Tuesday, Feb. 26, 11:59 pm: E-HW 07 Section 8.2 Law of Sines and Cosines
Due Thursday, Feb. 28, 11:59 pm: E-HW 08 Section 8.3 and 9.1
Due Tuesday, March 12, 11:59 pm: E-HW 09 Section 9.2 Identities
Due Tuesday, March 12: Writing Assignment 5: The Law of Sines and Cosines to the Rescue
Test 2 begins this week. See review sheet. This is in the folder Reviews for Exams on Blackboard.
Read: Section 9.3, 10.1 and 10.2
Do (for practice): Section 9.2 -- 13, 15, 27 - 30, 35, 54 - 58
Due tonight, Tuesday, March 12, 11:59 pm: E-HW 09 Section 9.2 Identities
Due Thursday, March 14
(extended): Writing Assignment 5: The Law of
Sines and Cosines to the Rescue
Test 2 continues this week. See review sheet. This is in the folder Reviews for
Exams on Blackboard.
NEW: You can have up to Friday, March 15 to take Test 2. Dates
have been extended. Note the hours of the Test Center.
- Mon., Mar. 11 9:00 AM -3:30 PM (it closes at 4:30 pm)
- Tues., Mar. 12 9:00 AM -3:30 PM (it closes at 4:30 pm)
- Wed., Mar. 13 9:00 AM-7:00 PM (it closes at 8:00 pm)
- Thurs., Mar. 14 9:00 AM-7:00 PM (it closes at 8:00 pm)
- Fri., Mar. 15 9:00 AM -3:30 PM (it closes at 4:30 pm)
Read: Section 12.1
Do (for practice): Section 9.3 -- 1-8, 17 , 18, Section 10.1 -- 4-25, 31, 37-50, 64, 65 and Section 10.2 -- 1-10, 12-34, 37-43, 47-49, 58, 82
Due Thursday, March 21, 11:59 pm: E-HW 10 Section 9.2 and 9.3
Due Tuesday, March 26, 11:59 pm: E-HW 11 Section 10.1-10.2 Composition, Decomposition, and Inverses
NEW: You can have up to Friday, March 15 to take Test 2. Dates have been extended. Note the hours of the Test Center.
- Mon., Mar. 11 9:00 AM -3:30 PM (it closes at 4:30 pm)
- Tues., Mar. 12 9:00 AM -3:30 PM (it closes at 4:30 pm)
- Wed., Mar. 13 9:00 AM-7:00 PM (it closes at 8:00 pm)
- Thurs., Mar. 14 9:00 AM-7:00 PM (it closes at 8:00 pm)
- Fri., Mar. 15 9:00 AM -3:30 PM (it closes at 4:30 pm)
Read: Section 12.1 and 12.2
Do (for practice): Section 12.1 -- 16-20, 24 and 12.2 -- 1-2, 4, 5, 8, 13-18, 21, 23, 25-27 and Chapter 12 Review -- 12, 29, 34, 35, 37
Due Thursday, March 21, 11:59 pm: E-HW 10 Section 9.2 and 9.3
Due Tuesday, March 26, 11:59 pm: E-HW 11 Section 10.1-10.2 Composition, Decomposition, and Inverses
Due Thursday, March 28, 11:59 pm: E-HW 12 Sections 12.1-12.2
Thursday, March 21: QUIZ 7 on 9.2 and 9.3
Read: Section 13.1 and 13.2
Do (for practice): Section 12.3 -- 1-13
Due tonight, Thursday, March 21, 11:59 pm: E-HW 10 Section 9.2 and 9.3
Due Tuesday, March 26, 11:59 pm: E-HW 11 Section 10.1-10.2 Composition, Decomposition, and Inverses
Due Thursday, March 28, 11:59 pm: E-HW 12 Sections 12.1-12.2 and E-HW 13 Section 12.3 Application of Vectors
Due Tuesday, April 2: Writing Assignment 6: Using Trig Identities
Here is an opportunity for rhinos who want better test scores.
Read: Section 13.3
Do (for practice): Section 13.1 -- 1-48
Due tonight, Tuesday, March 26, 11:59 pm: E-HW 11 Section 10.1-10.2 Composition, Decomposition, and Inverses
Due Thursday, March 28, 11:59 pm: E-HW 12 Sections 12.1-12.2
Due Thursday, March 28, 11:59 pm: E-HW 13 Section 12.3 Application of Vectors
Due Tuesday, April 2, 11:59 pm: E-HW 14 Section 13.1 Sequences
16
1
Due Tuesday, April 2: Writing Assignment 6: Using Trig Identities
Here is an opportunity for rhinos who want better test scores.
Thursday, March 28: QUIZ 8 on 10.1-10.2, 12.1-12.2
Read: Section 13.3
and 13.4
Do (for practice): Section 13.2
-- 1-30, 34-37, 42, 43, 45
Due tonight, Thursday, March 28, 11:59 pm:
- E-HW 12 Sections 12.1-12.2
- E-HW 13 Section 12.3 Application of Vectors
Due Thursday, April 4, 11:59 pm: E-HW 15 Section 13.2 Series
Due Tuesday, April 2: Writing Assignment 6: Using Trig Identities
Here is an opportunity for rhinos who want better test scores. Certain conditions apply.
Read: Section 14.1 (See BB for a link to this chapter.)
Practice on eHW Flash Cards:
Flash Card 13.3 Finite Geometric Series
Flash Card 13.4 Infinite Geometric Series - find the sum
Flash Card 13.4 Applications of Infinite Geometric Series
Optional: Section 13.3 -- 1-17, 20-26 and Section 13.4 -- 1-17, 24-26 and Chapter 13 Review -- 4-9
Due tonight, Tuesday, April 2, 11:59 pm: E-HW 14 Section 13.1 Sequences
Due Thursday, April 4, 11:59 pm: E-HW 15 Section 13.2 Series
Due Tuesday, April 9, 11:59 pm: E-HW 16 Section 13.3 and 13.4
Here is an opportunity for rhinos who want better test scores. (Last date available to retest is Friday, April 5.)
Thursday, April 4: QUIZ 9 on 13.1 and 13.2
Read: Section 14.2 and 14.3 (See BB for a link to this chapter or click on wiley.com/college/hughes-hallett)
Do: Section 14.1 -- 1-43
Practice on eHW Flash Cards:
Flash Card 14.1 Parametric Equations - Eliminate the Parameter
Flash Card 14.1 Parametric Equations - Use Graphs to Parametrize
Due tonight, Thursday, April 4, 11:59 pm: E-HW 15 Section 13.2 Series
Due Tuesday, April 9, 11:59 pm: E-HW 16 Section 13.3 and 13.4
Due Thursday, April 11, 11:59 pm: E-HW 17 Section 14.1
Here is an
opportunity for rhinos who want better test scores. (Last date
available to retest is Friday, April 5.)
Read: Section 14.4 (Click on wiley.com/college/hughes-hallett)
Do: Section 14.2 -- 1-26, 28, 29 and Section 14.3 -- 1-10, 11a, 18, 19
Due Tuesday, April 9, 11:59 pm: E-HW 16 Section 13.3 and 13.4
Due Thursday, April 11, 11:59 pm: E-HW 17 Section 14.1
Due Tuesday, April 16, 11:59 pm: E-HW 18 Section 14.2 and 14.3
Thursday, April 11: QUIZ 10 over 13.3-13.4 and 14.1
Due Thursday, April 18: Writing Assignment 7: Job Offer
Read: Section 14.4 (Click on wiley.com/college/hughes-hallett)
Do: Section 14.4 -- 1-4, 15, 16
Due tonight, Thursday, April 11, 11:59 pm: E-HW 17 Section 14.1
Due Tuesday, April 16, 11:59 pm: E-HW 18 Section 14.2 and 14.3
Due Tuesday, April 23, 11:59 pm: E-HW 19 Section 14.4
Due Thursday, April 18: Writing Assignment 7: Job Offer
See review sheet to prepare for Test 3 in the folder (Reviews for Exams)
Covers: Sections 10.1-10.2, 12.1-12.3. 13.1-13.4, 14.1-14.3 and Quiz 8, 9, and 10 and your eHW assignments 10 through 18.
The test is scheduled outside of class in the Math Test Center (KT G18). There is no class meeting on Tuesday, April 16.
(An optional review session will be held in KT 218 from 9 AM - 1 PM on Tuesday, April 16.)
Walk in with any kind of photo ID and your graphing calculator to take the test during these times:
- Tues., April 16 9:00 AM -3:30 PM (it closes at 4:30 pm)
- Wed., April 17 9:00 AM-7:00 PM (it closes at 8:00 pm)
- Thurs., April 18 9:00 AM-7:00 PM (it closes at 8:00 pm)
- Fri., April 19 9:00 AM -3:30 PM (it closes at 4:30 pm)
No appointment is necessary. You can only take the test in one sitting. No notes or formula sheet, although one will be provided. You will have unlimited time to take it, constrained only by the hours of the test center. For example, arriving at 3:30 PM on Monday, Tuesday, or Friday or arriving at 7:00 PM on Wednesday or Thursday provides only one hour to complete the test (not recommended).
You may use the time to take Test 3 in the Math Test Center (KT G18) or come to an optional review session in KT 218 from 9 AM - 1 PM
Due Thursday, April 18: Writing Assignment 7: Job Offer.
Read: Section 9.6
Do: Section 14.4 -- 5-8 and Section 9.6 -- 1-23, 27, 36-39
Due Tuesday, April 23, 11:59 pm: E-HW 19 Section 14.4
Due Thursday, April 25, 11:59 pm: E-HW 20 Section 9.6
Tuesday, April 23: QUIZ 11 over 14.4
Videos (all optional):
Complex numbers take us out of our one dimensional world. This video shows where the function f(x) = x2 + 1 crosses the x-axis.
This video gives an entertaining history.
This video uses 3-D animations to show complex number arithmetic:
Here is one application involving AC circuits.
Due tonight, Tuesday, April 23, 11:59 pm: E-HW 19 Section 14.4
Due Thursday, April 25, 11:59 pm: E-HW 20 Section 9.6
Rhino Opportunity for Late Assignments - Missed an assignment or want to improve your score on a past assignment? For each perfect score you earn before the due date in the "Assignments (for a Grade)" area, you may redo one assignment at a 10% late penalty. All due 11:59 PM Sunday, April 28.
Final Exam:
9:00 Section: Thursday, May 2 from 8:00 AM - 10:00 AM, KT 218
10:30 Section: Tuesday, April 30 from 10:30 AM - 12:30 PM, KT 218
(You may come to either one of these but please ask if there is room.)
QUIZ 12 Thursday, April 25 on 9.6
Rhino Opportunity for Late Assignments - Missed an assignment or want to improve your score on a past assignment? For each perfect score you earn before the due date in the "Assignments (for a Grade)" area, you may redo one assignment at a 10% late penalty. All due 11:59 PM Sunday, April 28.
Final Exam:
9:00 Section: Thursday, May 2 from 8:00 AM -
10:00 AM, KT 218
10:30 Section: Tuesday, April 30 from 10:30 AM - 12:30 PM,
KT 218
(You may come to either one of these but please ask if there is room.)
See the review packet in the folder Reviews for Exams on Blackboard.
Euler Extra Credit due the day of your final exam.