Trigonometry and College Algebra

MTH13
D02 Section 51468
Tuesday, Thursday, 2:00 pm - 3:50 pm, room CP 309
 

 
05/21
Thursday
Second Part of the Final Exam

start time: 2:00 pm
end time: 3:15 pm

go to myLab, find Final Exam Part 2 in the homeworks.
 
05/19
Tuesday
First Part of the Final Exam

start time: 2:00 pm
end time: 3:15 pm

go to myLab, find Final Exam Part 1 in the homeworks.
 
Weeks 14 - 16

Updated office hours: Tuesdays, 4 pm - 5 pm and Fridays, 11 am - 12 pm

Our Tutor: Mamadou
Days: Thursdays, 5pm - 9pm
Blackboard collaborate link: https://us.bbcollab.com/collab/ui/session/guest/8cc96a363c9c43dfb37e84581f9831c4
If you need to dial-in, here is the number +1-571-392-7650 PIN: 393 526 6760

Here you can find the quizzes grades.
05/14
Thursday
Preparing for the Final Exam / Review

We will work on the Sample Final Exam 2

recording link

Final Grade will be composed of the following weights:
Quizzes/Homeworks (4 worst scores dropped) average: 34%
Midterm Exam: 33%
Final Exam: 33%
 
 
05/12
Tuesday
Preparing for the Final Exam / Review

recording link

We finished working on the Sample Final Exam 1

On this day, from 7 am to 7 pm you can take the Midterm Extra Points test at myLab.
The test has 10 questions, 2 points each, so you can earn up to 20 points towards your Midterm Exam Score. Note that the Midterm Exam Score can be improved up to 100% / points only.
The test is timed at 60 minutes. You have only one attempt.
 
05/07
Thursday
Preparing for the Final Exam / Review

We went over the first 7 problems of the Sample Final Exam 1

Recording link
 
05/05
Tuesday
We will covered
Section 5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically
Note that in 11th edition, it is section 5.5
Section 5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants
Note that in 11th edition, it is section 5.6

Lecture slides: MTH13-Section5_5.pdf, MTH13-Section5_6.pdf (slides are corrected!)

Also, I take my comment back: the example is the same in both sections!

Videos:
Section 5.5 (11th Edition) or 5.6 (10th Edition)
Section 5.6 (11th Edition) or 5.7 (10th Edition)

Addditional videos from Khan Academy:
1) The standard method for finding the deteminant of the 3x3 matrix (video, ~4 mins).
Note that it is different from the one I showed - I used the first column for the coefficients, and in the video, the first row is used. Both methods work just fine!
2) The shortcut method for finding the determinant of a 3x3 matix (video, ~ 3mins)
3) Finding he determinant of the 3x3 matrix (practice)
4) Solving system of three linear equations in three variables using addition/elimination method (video, ~8 mins)
5) Solving system of three linear equations in three variables using addition/elimination method: another example (video, ~7 mins)

Additional videos from YouTube:
1) Solving the system of linear equations in three unknowns using Cramer's rule (video, ~15 mins)
2) Another person s solving a system of three equations in three unknowns using the Cramer's rule (video, ~8.5 mins)

Homework 14 : based on Section 5.6 only, at MyLab
timed at 40 mins, only one attempt, due: Friday, May 15th, 11:59pm.


04/30
Thursday
We covered
Section 5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants
Note that in 11th edition, it is section 5.4

Lecture slides: MTH13-Section5_4.pdf

Video recording: https://youtu.be/6p7K9-DSYpg

Additional video and practice from Khan Academy:
1) Finding the determinant of the 2x2 matrix (video, ~ 1 min)
2) Finding the determinant of the 2x2 matrix (practice )

Additional video from YouTube:
Solving the system of linear equations in two unknowns using Cramer's rule

Quiz 13 or Homework 13 : based on Section 5.5 at MyLab
timed at 40 mins, only one attempt, due: Tuesday, May 12th, 11:59pm.
HW 18
(due date: Tuesday, May 12th)


Section 5.4 / 10, 26, 34 (11th Edition), or
Section 5.5 / 10, 26, 34 (10th Edition)

Solutions: MTH13-Section5_4.pdf
04/28
Tuesday
Review of Chapters 10 and 20 (Trigonometric Functions)

Review slides: MTH13-Chapters10_20Review.pdf
5 more examples: MTH13-Chapter20MoreReviewProblems.pdf

Videos: https://youtu.be/26t8nLGj4BY
 
Week 13

My office hours: Mondays, 2 pm - 3 pm and Tuesdays, 1pm - 2pm

Our Tutor: Mamadou
Days: Thursdays, 5pm - 9pm
Blackboard collaborate link: https://us.bbcollab.com/collab/ui/session/guest/8cc96a363c9c43dfb37e84581f9831c4
If you need to dial-in, here is the number +1-571-392-7650 PIN: 393 526 6760
04/23 We covered:
Section 20.6 The Inverse Trigonometric Functions

Lecture slides: MTH13-Section20_6.pdf

Videos:
Section 20.5 discussion (quick review), ~ 6 mins
Section 20.6 recording

Quiz 12 or Homework 12 : based on Section 20.6 at MyLab
timed at 40 mins, only one attempt, due: Friday, May 8th, 11:59pm.
HW 17
(due date: Friday, May 8th)


Section 20.6 / 12, 18, 24, 26, 31, 39, 42

Solutions: MTH13-Section20_6.pdf
04/21 We covered:
Section 20.5 Solving Trigonometric Equations

Please note that we will not meeting online. Instead, I will post videos - see all of them below. Make sure you see them before our Thursday meeting.


Lecture slides: MTH13-Section20_5.pdf

Videos:
Introduction + example 1 (~ 6 mins)
Examples 2-3 (~16.5 mins)
Examples 4-5 (~17 mins)

Quiz 11 or Homework 11: based on Section 20.5 at MyLab
timed at 40 mins, only one attempt, due: Tuesday, May 5th, 11:59pm.

Other online resources: to be posted
HW 16
(due date: Tuesday, May 5th)


Section 20.5 / 6, 10, 12

Solutions: MTH13-Section20_5.pdf
Week 12

My office hours: Mondays, 2 pm - 3 pm and Tuesdays, 1pm - 2pm

Our Tutor: Mamadou
Days: Thursdays, 5pm - 9pm
Blackboard collaborate link: https://us.bbcollab.com/collab/ui/session/guest/8cc96a363c9c43dfb37e84581f9831c4
If you need to dial-in, here is the number +1-571-392-7650 PIN: 393 526 6760
04/16 We covered:
Section 20.4 Half-Angle Formulas

Lecture slides: MTH13-Section20_4.pdf


Video recordings links:
Section 20.3, part 2
Section 20.4

Quiz 10 or Homework 10 : based on Sections 20.3 and 20.4 at MyLab
timed at 40 mins, only one attempt, due: Friday, May 1st, 11:59pm.
HW 15
(due date: Friday, May 1st)


Section 20.4 / 8, 10, 22, 28, 32

Solutions: MTH13-Sections20_3-20_4.pdf
04/14 We covered:
Section 20.2 The Sum and Difference Formulas
Section 20.3 Double-Angle Formulas

Video recordings:
Section 20.2: https://youtu.be/q_r_ygF9K00
Section 20.3 (part 1) : https://youtu.be/RQ1DXJ8NJtQ

Lecture slides: MTH13-Section20_2.pdf (updated on 04/19 at 8pm), MTH13-Section20_3.pdf

Trigonometric table

Quiz 9 or Homework 9 : based on Section 20.2 at MyLab
timed at 40 mins, only one attempt, due: Tuesday, April 28th, 11:59pm.

Online resources:
1) Finding trig values using angle addition identities (video, ~8.5 mins)
  guided practice: 4 problems
2) Using sum formula (video, ~6 mins)
HW 14
(due date: Tuesday, April 28th)


Section 20.2 / 4, 6, 12, 22, 32,
Section 20.3 / 12, 16, 28, 30, 34

Solutions: MTH13-Section20_2.pdf, MTH13-Sections20_3-20_4.pdf
Week 11 - Spring Break

My office hours: Mondays, 2 pm - 3 pm and Tuesdays, 1pm - 2pm

Our Tutor: Mamadou will be available during Spring break!
Days: Thursdays, 5pm - 9pm
Blackboard collaborate link: https://us.bbcollab.com/collab/ui/session/guest/8cc96a363c9c43dfb37e84581f9831c4
If you need to dial-in, here is the number +1-571-392-7650 PIN: 393 526 6760
Note that the tutor is working one-on-one. I was told that it is the best to schedule the meetings with him through Starfish (although not necessary) .

We will not be meeting this week, however I will be available during the office hours, as well as our tutor.


Be safe and well! Enjoy the break! See you on Tuesday, April 14th!
Week 10

My office hours: Mondays, 2 pm - 3 pm and Tuesdays, 1pm - 2pm

Our Tutor: Mamadou
Days: Thursdays, 5pm - 9pm
Blackboard collaborate link: https://us.bbcollab.com/collab/ui/session/guest/8cc96a363c9c43dfb37e84581f9831c4
If you need to dial-in, here is the number +1-571-392-7650 PIN: 393 526 6760
04/02 We covered:
Section 20.1 Fundamental Trigonometric Identities


Video Recording link: https://youtu.be/E8-Wo5hR6sI

Lecture slides: MTH13-Section20_1.pdf

Quiz 8 or Homework 8: based on Section 20.1at MyLab
timed at 40 mins, only one attempt, due: Thursday, April 23rd, 11:59pm.

Online materials:
1) Using trigonometric identities (video, ~3 mins)
HW 13
(due date: Tuesday, April 14th)


Section 20.1 /
12 (#16 in Solutions 1),
16 (#16 in Solutions 2),
19 (similar to # 12 from Solutions 1),
24 (# 24 in Solutions 2),
30 (#24 in Solution 1 or #30 in Solutions 2),
38 (# 34 in Solutions 1),

Solutions 1: MTH13-Section20_1_v1.jpg
Solutions 2: MTH13-Section20_1_v2.pdf
03/31 We covered:
Section 10.4 Graphs of y = tan x, y = cot x, y = sec x, and y = csc x
Section 10.5 Applications of the Trigonometric Graphs

Video recording link: https://youtu.be/_X5Ta9jcBLo

Lecture slides: MTH13-Sections10_4-10_5.pdf

Quiz 7 or Homework 7: based on Sections 10.4 and 10.5 at MyLab
timed at 40 mins, only one attempt, due: Tuesday, April 21st, 11:59pm.
HW 12
(due date: Tuesday, April 14th)


Section 10.4 / 12, 14 (change 60 to 6), sketch two cycles of y = 0.30 sin (0.5 π t) (#16 in solutions),
Section 10.5 / 3 (10th edition) or 7 (11th edition), 10 (10th edition) or 14 (11th edition)

Solutions: Section 10.4, Section 10.5 will be posted shortly
Week 9

03/26 We covered:
Section 10.1 Graphs of y = a sin x and y = a cos x
Section 10.2 Graphs of y = a sin bx and y = a cos bx
Section 10.3 Graphs of y = a sin(bx+c) and y = a cos(bx+c)


Recorded meeting link: https://us-lti.bbcollab.com/recording/8bb5407412454fa78c8f20b542d43429

Lecture slides: MTH13-Sections10_1-10_3.pdf (they had some typos, now they are fixed)

Quiz 6: based on Sections 10.1 - 10.3 at MyLab
timed at 40 mins, only one attempt, due: Thursday, April 16th, 11:59pm.

Our Tutor: Mamadou
Days: Thuesdays, 5pm - 9pm
Blackboard collaborate link: https://us.bbcollab.com/collab/ui/session/guest/8cc96a363c9c43dfb37e84581f9831c4
If you need to dial-in, here is the number +1-571-392-7650 PIN: 393 526 6760

Online materials (choose the ones you think you need):
1) Graph of sin function (9:21 mins, video)
2) Features of sinusoidal functions (4:57 mins video, discussing amplitude, period and midline, the last one we didn't cover and I will not ask about it, but it is an easy feature of the graph)
3) Practice: amplitude of sinusoidal functions from graph (guided practice)
4) Practice: period of sinusoidal functions from graph (guided practice)
5) Amplitude and period of sinusoidal functions from equation (8:20 mins, video)
    Note that from that page, in the menu on the left you will see link to two more videos:
      Transforming sinusoidal graphs: vertical stretch & horizontal reflection (12:51 mins) and
      Transforming sinusoidal graphs: vertical & horizontal stretches (10:42 mins), and
    three practices:
      Amplitude of sinusoidal functions from equation
      Midline of sinusoidal functions from equation (you can skip this one since we are not doing midlines)
      Period of sinusoidal functions from equation
6) Practice: graph sinusoidal functions (guided practice)
7) Practice: Graph sinusoidal functions: phase shift (guided practice)
HW 11
(due date: Thursday, April 9th)


Sections 10.1 and 10.2 (pdf file),
Section 10.3 / 8, 14 (change the sing in this problem to +, instead of -)

Solutions: Sections 10.1 and 10.2, Section 10.3
03/24 Midterm Exam

Midterm Exam Questions: MTH13-MidtermExam2020-03.pdf
The test time is two hours; 30 minutes are to make sure that you send everything to my e-mail by 4:30pm.

Blackboard Collaborate link (if you have any questions, I'm available online!)

Start time: 2 pm
End Time: 4:30 pm
Send all your work (take pictures or scan your work) to my e-mail address: natna20@gmail.com
Warning: you must send everything to my e-mail address by 4:30 pm sharp!
 
Week 8 - instructional recess for distance-learning preparation
March 12 - March 18th


03/19 Video session: Midterm Exam Review

Blackboard Collaborate link: https://us.bbcollab.com/guest/18b0bf92b8724c8eb7a263bc66305253
(use it to join the video session)

instructions:
1) join the session 5-10 minutes in advance, look around for the tools that are available to you!
2) when you join the session, both microphone(share audio) and camera(share video) are turned off. So if you want to ask the question, make sure you turn the audio on.
3) you can also join these video meetings when you log-in into our Blackboard page.

Slides from the meeting: MTH13MidtermExamReviewSlides.pdf
Video recording from our meeting:
Talking about the Midterm Exam (format and other details)
Chapter 3: Question 1
Chapter 3: Question 2
Chapter 3: Question 3
Chapter 13: Question 1
Chapter 13: Question 2
Chapter 13: Question 3
Chapter 13: Question 4 (note that I have a typo in slides: it was marked as question 3)
Chapter 9: Question 1
Chapter 9: Question 2 (I forgot to turn on the recording so it is "half-way" through the problem)
Chapter 12: Question 1
Chapter 12: Question 2 (we didn't do it at our online meeting, recorded video-solution)
Chapter 12: Question 3 (we didn't do it at our online meeting, recorded video-solution)
03/13 Dear All,
The classes will resume on Thursday, March 19th in a distance-learning form.

Please fill out this Google Form by tomorrow evening, March 14th!

During this recess, please prepare for the Midterm Exam! The new date is Tuesday, March 24th, the format will be posted.

Here are all the materials needed:

1) Review problems, with answers a the back, for Chapters 3 and 13: Chapters3_13Review.pdf
    Solutions (scanned): Chapter3_13ReviewSolutions.pdf

2) Miderm Exam Review problems (same as on the Midterm Exam and Final Exams page): MTH13-MidtermExam-sample.pdf
Solutions: Chapters 9 and 12, MTH13-MidtermExam-sampleCh3_13-sols-page1.jpg (a picture), MTH13-MidtermExam-sampleCh3_13-sols-page2.jpg (a picture) MTH13-MidtermExam-sampleCh3_13-sols-page3.jpg (a picture)

Planned meetings for the next two weeks:
Thursday, March 19th, 2 pm - 4pm.
    Online meeting. I will invite you to Blackboard Collaborate. You don't need to log-in to Blackboard. I will just post a link here. Follow it.
    If you have any questions about the review problems, this is the moment to ask them!
Tuesday, March 24th, TIME TBA
    Midterm Exam, the format will be posted (I'm working on it)

All your grades are and will be available at Google Sheets
Week 7

Midterm Exam will be based on material from Chapters 3, 9, 12, and 13.
03/12 Review of Chapters 3 & 13 - cancelled

The class is cancelled. BCC will have a five-day instructional recess March 12-18.
The online classes resume on Thursday, March 19th.

Meanwhile,
1) check that you are receiving messages from me! (I send them through CUNY First),
2) Here, at Google Sheets I will be putting all the grades.
Use the last 4 digits of your school ID (EmployID) to see your scores
3) I'm planning to have live stream lectures at the time of our scheduled classes. More info will be posted.
4) I'm still deciding what to do with the quizzes and midterm exam.
 
03/10 We will cover:
Section 13.5 Natural Logarithms
Section 13.6 Exponential an Logarithmic Equations

Useful links:
1) Change of base: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:change-of-base/v/change-of-base-formula
2) Solving exponential equations using logarithms: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:exp-eq-log/v/exponential-equation
3) Solving logarithmic equations: https://www.khanacademy.org/math/algebra-home/alg-exp-and-log/alg-logarithmic-equations/v/solving-logarithmic-equations

HW 10
(due date: Thursday, March 19th)


Section 13.5 / 3, 9, 16, 21, 45, 53 (#51 in solutions),
Section 13.6 / 4, 10, 14, 18 (#16 in solutions), 23, 28 (#26 in solutions), 32 (#30 in solutions)

Solutions: Sections13.5 and 13.6
Week 6

Midterm Exam will be based on material from Chapters 3, 9, 12, and 13.
03/05 We covered:
Section 13.3 Properties of Logarithms

Useful link at Khan Academy: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-prop/v/introduction-to-logarithm-properties

At the end of the class we will have quiz 5 based on Sections 3.1, 3.2, and 3.4 (HWs 8 and 9)

Plan for the next few weeks:

T, 03/03: Sections 13.1 - 13.2
Th, 03/05: Section 13.3

T, 03/10: Sections 13.4 - 13.5
Th, 03/12: Review of Chapters 3 & 13

T, 03/17: Midterm Exam
HW 9
(due date: Thursday, March 12th)


Section 13.3 / 16, 18, 20, 28, 34, 46

Solutions: Section 13.3
03/03 We covered:
Section 13.1 Exponential Functions
Section 13.2 Logarithmic Functions

Useful link: A series of videos and practices abot the logarithms and exponential form: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-intro/v/logarithms
HW 8
(due date: Thursday, March 10th)


Section 13.1 / 7, 9, 11, 13, 18 (#14 in solutions), 22 (#18 in solutions)
Section 13.2 / 8, 14, 22, 34, 36, 46

Solutions: Section 13.1, Section 13.2
Week 5

Midterm Exam will be based on material from Chapters 3, 9, 12, and 13.

Midterm Exam review problems
02/27 We will cover:
Section 3.4 The Graph of a Function

At the end of the class we had quiz 4 based on Sections 12.3-12.6 (HWs 5, 6, and 7)
HW 9
(due date: Thursday, March 5th)


Section 3.4 / 6, 20, 22, 30 (change to y = 2 / (x+2) ), 52 (#50 in solutions), 64 (#60 in solutions)

Solutions: Section 3.4
02/25 We will cover:
Section 3.1 Introduction to Functions
Section 3.2 More about Functions

Some useful links:
1) Domain and range of functions (videos + practice)
2) Evaluating functions (video + practice)
HW 8
(due date: Tuesday, March 3rd)


Section 3.1 / 13, 15, 24,
Section 3.2 /8, 15, 18, 22 (#20 in solutions), 26 (#24 in solutions)

Solutions: Section 3.1, Section 3.2
Week 4
02/20 Review of Chapter 9 and 12 material

We went over problems 2, 6, 14, 43 and 49 from Chpater Review, and problem 1 from Chapter Practice Test.

We did problems 4, 7, and 14 from the Chapter 12 Review, the rest: 28, 34, 42, 46, 57, 63, 68, 70 and 72 I suggested to work on your own. Here are the solutions with answers: Chapter 12 Review

At the end of the class we had quiz 3 based on Sections 12.1 and 12.2 (HW 4)
 
02/18 We will finish Section 12.6 Products, Quotients, Powers, and Roots of Complex Numbers
and
Review chapters 9 and 12
HW 7
(due date: Tuesday, February 25th)


Section 12.6 / 42
Week 3

Note that on Wednesday, February 12th the college is closed - Lincoln's birthday
on Monday, February 17th the college is closed - President's day
 
02/13 We will cover:
Section 12.5 Exponential Form of a Complex Number
Section 12.6 Products, Quotients, Powers, and Roots of Complex Numbers

At the end of the class we will have quiz 2 based on Sections 9.2 and 9.3 (HW 2)
HW 6
(due date: Tuesday, February 18th)


Section 12.5 / 16, 32, 34, 36;
Section 12.6 / 5, 7, 9, 11, 17, 26, 32

Solutions: Section 12.5, Section 12.6
02/11 We will cover:
Section 12.3 Graphical Representation on Complex Numbers
Section 12.4 Polar Form of Complex Numbers

Useful links:
1) Absolute value (magnitute) and angle of complex numbers (videos + practice)
- the process is similar to convertion from rectangular form to poar form (only we keep the degrees, not radians)
2) Polar and rectangular form (coverting from one to another) (video + practice)
- note that they are working with radians, whereas we are working with degrees.
3) Multiplication, division, powers of complex numbers in polar form (videos + text + practices) + exponential form
HW 5
(due date: Tuesday, February 18th)


Section 12.3 / 8, 16, 26;
Section 12.4 / 12, 18, 22, 34

Solutions: Section 12.3, Section 12.4
Week 2
02/06 We will cover:
Section 12.1 Basic Definitions
Section 12.2 Basic Operations with Complex Numbers

Some useful links:
1) Parts of complex numbers (practice)
2) Multiplying compex numbers (text + practice)
3) Dividing complex numbers (video + practice)
4) Adding and subtracting complex numbers (videos + practice)
HW 4
(due date: Thursday, February 13th)


Section 12.1 / 6, 11, 14, 20, 26, 35, 56, 67;
Section 12.2 / 8, 16, 22, 30

Solutions: Section 12.1, Section 12.2
02/04 We will cover:
one more example from Sections 9.3 Vector Addition by Components
Section 9.4 Applications of vectors

At the end of the class we will have quiz 1 based on Section 9.1 (HW 1)
HW 3
(due date: Tuesday, February 11th)


Section 9.4 exercises: 8, 10, and

(9th edition book, problem 4): To straighten a small tree, two horizontal ropes perpendicular to each other are attached to the tree. If the tensions in the ropes are 18.5 lb and 23.0 lb, what is the resultant force on the tree?

Answers and solutions: Section 9.4
Week 1
01/30 We will cover:
Section 9.2 Components of Vectors
Sections 9.3 Vector Addition by Components

Useful link: more about vectors at Khan Academy: https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/vectors/v/vector-introduction-linear-algebra
HW 2
(due date: Thursday, Feb. 6th)


8th, 9th and 10th Editions:
Section 9.2 exercises: 6, 18, 22
Section 9.3 exercises: 4, 12, 28

Answers and solutions: Section 9.2, Section 9.3
01/28 Welcome to the MTH 13 course!

During this week make yourself familiar with this web site!
In case if you miss a class, this is the place to visit and see what we covered, what is the homework assignment. In addition, any announcements I made in class will be also posted here.

The first two chapters (Chapter 9 and 10) of our book are available online through our library e-reservses:
http://bcc-cuny.libguides.com/er.php?course_id=37618#
Note that there will be no excuses made due to you not having a book, since the first two chapters are immediately available to you at our library!

Today we covered:
part of Section 9.1 Introduction to Vectors

Useful link: see video about difference between Vectors and Scalars:
http://www.khanacademy.org/video/introduction-to-vectors-and-scalars?topic=physics-1

Grid paper: grid-lined-paper.pdf
HW 1
(due date: Tuesday, Feb. 4th)


8th Edition: p. 263 / 14, 24, 28, 32
9th Edition: pages 258 - 259 / 14, 24, 28, 32
10th Edition: pages 261 - 262 / 14, 24, 28, 32

Answers and solutions: MTH13-Section9_1.pdf