Trigonometry Videosmr. Mackenzie's Web Page
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• Old Versions of Chapters 0 and 1
WEEK #1 - Proving Trigonometric Identities. NOTES - My notes in pdf format Video - Verifying Trig Identities Video - Verifying a trigonometric identity with multiple steps.
Preliminaries: (3-page intro + 44 pages) …Part 1: Logic…Part 2: Basic Algebra I … Part 3: Basic Algebra II … Factoring 'Handout': This is already part of the notes, but here's the handout as a separate file. Section A.3: Factoring problems: Factoring.pdf
- Trigonometry helps us find angles and distances, and is used a lot in science, engineering, video games, and more! Right-Angled Triangle. The triangle of most interest is the right-angled triangle. The right angle is shown by the little box in the corner: Another angle is often labeled θ, and the three sides are then called.
- Mackenzie's Web Page: Math and Physics Home Calculus Physics 11 Physics 12 Math 12 Helpful Resources Trigonometry Videos Kinematics 1. Unique website with.
Trigonometry Videosmr. Mackenzie's Web Page Pdf
Chapter 1: Functions and Their Graphs (108 pages) …
News (2021-01-05) Cleaned up the web page to make it less hideous and more consistent with the revamped page for Elementary Calculus. (2015-07-19) After spending quite a bit of time trying to compile the book correctly with TeX Live 2014—and not succeeding—I decided to give up and go back to TeX Live 2011. The Map of Early Modern London comprises four distinct, interoperable projects. MoEML began in 1999 as a digital atlas of sixteenth- and seventeenth-century London based on the 1560s Agas woodcut map of the city.
Chapter 1: Functions (167 pages)
• CORRECTION to 1.2.3! In the middle of page 1.2.3, -9 (instead of 9) is not in the domain of f.
BIG FILES:Sections 1.1-1.4 … Sections 1.5-1.11
SMALLER FILES (for faster download):
Sections 1.1-1.2 … Rectangular Coordinates; Graphs of Equations and Circles
Sections 1.3-1.4 … Graphs and Lines ; Functions
Sections 1.5-1.7 … Analyzing Graphs of Functions; A Library of Parent Functions; Transformations
Sections 1.8-1.9 … Combining Functions; Inverse Functions
Sections 1.10-1.11 ... Mathematical Modeling and Variation
Sections 1.1, 1.2, and 1.3 in Larson: ; …
Section 1.4 in Larson: …
Sections 1.5 in Larson: Analyzing Graphs of Functions: Part 1 … Part 2 … Part 3…
Section 1.6 in Larson: A Library of Parent Functions…
Section 1.7 in Larson: …
Section 1.8 in Larson: …
Sections 1.9 and 1.10 in Larson: ;
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• Chapter 2: Polynomial and Rational Functions (about 82 pages)
BIG FILES:Sections 2.1-2.4 … Sections 2.5-2.7
SMALLER FILES (for faster download):
Section 2.1 in Larson: Quadratic Functions (and Parabolas)
Section 2.2 in Larson: Polynomial Functions of Higher Degree
Section 2.3 in Larson: Long and Synthetic Polynomial Division
Section 2.4 in Larson: Complex Numbers
Section 2.5 in Larson: Finding Zeros of Polynomial Functions
Part 1 … Part 2 … Section 2.5, Part 3 (New! The QF Method for Factoring Quadratics)
• MINOR CORRECTION: Section 2.5, Notes 2.55: Factor … over C and find all of its complex zeros.
Section 2.6 in Larson: Rational Functions
Section 2.7 in Larson: Nonlinear Inequalities
• Chapter 3: Exponential and Log Functions (40 pages)
BIG FILE:Chapter 3
SMALLER FILES (for faster download):
Section 3.1 in Larson: Exponential Functions and Their Graphs
Section 3.2 in Larson: Log Functions and Their Graphs
Section 3.3 in Larson: (More) Properties of Logs
Sections 3.4 and 3.5 in Larson: Exponential and Log Equations and Models
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TRIG NOTES
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• Chapter 4: Trigonometry (Intro) (93 pages)
BIG FILES:Sections 4.1-4.4 … Sections 4.5-4.6 … Sections 4.7-4.8 … Handout #1 (Basic IDs)
SMALLER FILES (for faster download):
Section 4.1 in Larson: (Angles); Radian and Degree Measure
Sections 4.2-4.4 in Larson: Trig Functions (Values and Identities): Part 1 … Part 2
Basic Trig IDs (handout in class): Basic Trig IDs (also in 5.1 notes)
Visualizing the Six Basic Trig Functions: http://www.kkuniyuk.com/TrigSixParts.pdf (corrected late 2/11/06)
Section 4.5 in Larson: Graphs of Sine and Cosine Functions: Part 1 … Part 2
Section 4.6 in Larson: Graphs of Other Trig Functions: Part 1 … Part 2
Section 4.7 in Larson: Inverse Trig Functions
Smaller files for older computers: Part 1 … Part 2
Section 4.8 in Larson: Applications
• Chapter 5: Analytic Trig (61 pages)
BIG FILES:Sections 5.1-5.3 … Sections 5.4-5.5 and IDs
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SMALLER FILES (for faster download):
Section 5.1 in Larson: Fundamental Identities (IDs)
Basic Trig IDs (also in Ch.4, 5.1): Basic Trig IDs
Section 5.2 in Larson: Verifying Trig IDs
Section 5.3 in Larson: Solving Trig Equations: Part 1 … Part 2
Sections 5.4 and 5.5 in Larson: More Trig Ids
Trig IDs:Handout #1 (Basic IDs) … Handout #2 (Advanced IDs)
Trigonometry Videosmr. Mackenzie's Web Page Template
• Chapter 6: Additional Topics in Trig (38 pages of primary notes)
BIG FILE:Chapter 6
SMALLER FILES (for faster download):
Section 6.1 in Larson: The Law of Sines
Section 6.2 in Larson: The Law of Cosines
Flowchart for Sections 6.1 and 6.2 (better for practical use than actual 'memorization'): M1410601Chart.pdf
Section 6.3 in Larson: Vectors in the Plane
Section 6.4 in Larson: Vectors and Dot Products
Section 6.5 in Larson: Trig Form of a Complex Number
Related 'Handout' (not handed out in class, though; print it!): M1410605Handout.pdf
Khan Academy on Euler’s Formula (Do you have emotion?)
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MORE ALGEBRA NOTES;
LINEAR ALGEBRA NOTES
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• Chapter 7: Systems and Inequalities
BIG FILE:Chapter 7
SMALLER FILES (for faster download):
Sections 7.1-7.3 in Larson: Systems of Equations
Section 7.4 in Larson: Partial Fractions: Part 1 … Part 2
Sections 7.5-7.6 in Larson: Graphing Inequalities and Linear Programming
• Chapter 8: Matrices and Determinants
BIG FILE:Chapter 8
• CORRECTIONS: Page 8.58 (top): Pierre [not George] Sarrus. Page 8.60 (middle): “lower left [not right] corner.”
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SMALLER FILES (for faster download):
Section 8.1 in Larson: Matrices and Systems of Equations
Smaller files for older computers: Part 1 … Part 2
Section 8.2 in Larson: Matrix Operations
Section 8.3 in Larson: Matrix Inverses
Section 8.4 in Larson: Determinants
Section 8.5 in Larson: Applications of Determinants
• Chapter 9: Discrete Math
BIG FILE:Chapter 9
SMALLER FILES (for faster download):
Sections 9.1 and 9.6 in Larson: Sequences, Series, and Counting
• FIBONACCI SCULPTURE: http://sfglobe.com/2015/01/14/3d-printed-sculptures-look-alive-when-spun-under-a-strobe-light/
Sections 9.2 and 9.3 in Larson: Arithmetic and Geometric Sequences, Partial Sums, and Series
• QIX AND FILLING IN A BOX (GEOMETRIC SERIES TALK)
• Sample game: https://www.youtube.com/watch?v=Wvzyd0OZg1I
• Winner! (2x) https://www.youtube.com/watch?v=RGSPj3vlR6M
Section 9.4 in Larson: Mathematical Induction
• THE HEART OF INDUCTION: https://www.youtube.com/watch?v=p_E3feHZtZM
Section 9.5 in Larson: Binomial Theorem
The Beauty of Pascal's Triangle: The Magic of Pascal's Triangle (Plinko from The Price is Right and Word Jumbles)
• Chapter 10: Conics and Polar Coordinates (handwritten; in progress)
BIG FILE:Chapter 10
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PRECALCULUS TESTS
(ALGEBRA TESTS and TRIG TESTS)
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Old Exams and Solutions (Spring 2016) – will be deleted in January 2017 (?)
Quiz 1A …Solutions (1 hour and 15 minutes)
• Chapter 0: Preliminary Topics
Quiz 1B …Solutions (45 minutes)
• Chapter 1: Functions
Midterm #2 …Solutions (50 minutes for Part 1; 1 hour and 20 minutes for Part 2)
• Chapter 2: Polynomial and Rational Functions
• Chapter 3: Exponential and Logarithmic Functions
Midterm #3 …Solutions (30 minutes for Part 1; 1 hour and 40 minutes for Part 2)
• Chapter 4: Trigonometry
Midterm #4 …Solutions (45 minutes for Part 1; 1 hour and 25 minutes for Part 2)
• Chapter 5: Analytic Trigonometry
• Chapter 6: Additional Topics in Trigonometry
Final …Solutions (2 hours and 20 minutes). Material covered in later terms may differ.
• Chapter 7: Systems of Equations [and Inequalities]
• Chapter 8: Matrices and Determinants
• Chapter 9: Discrete Math
• Chapter 10: Conics and Polar Coordinates [as time permits]
Front Matter, Notation, and Chapter 0: Preliminary Topics (99 pages)
BIG FILE:Chapter 0(revised 1/27/13)
SMALLER FILES (for faster download): Sections 0.1-0.5 … Sections 0.6-0.10 … Sections 0.11-0.16
Factoring 'Handout': Factoring.pdf: This is already part of the notes (in Section 0.7), but here's a separate file.
• CORRECTED ON 1/27/13: On the bottom of page 0.2.2, when the converse is declared to be false, Z and Q should be switched.
• Chapter 1: Functions (167 pages)
• CORRECTION to 1.2.3! In the middle of page 1.2.3, -9 (instead of 9) is not in the domain of f.
BIG FILES:Sections 1.1-1.4 … Sections 1.5-1.11
SMALLER FILES (for faster download): Sections 1.1-1.2 … Sections 1.3-1.4 … Sections 1.5-1.7 … Sections 1.8-1.9 … Sections 1.10-1.11
You’d see a thousand papers
Filled with broken poetries
And deadbeat proses
Full of woeful verses
With mournful pieces
Of unfinished stories
That are yet to be written
And failed to be spoken;
If you could read my mind,
You’d hear horrible screams
And earsplitting weeps
From shattered dreams,
Kept in a nasty notepad,
Scribbled on a bed
Of bloodstained words,
Ringing in my head.
If you could read my mind,
You’d see the shadows
That lurk within me;
You’d hear the bellows,
Screeching the words
“I’m tired,”
“I’m a failure,”
“I’m stupid –”
I know it sounds stupid,
It’s pathetically foolish
And seems like *******.
If you could read my mind,
You’d feel the tears
I had ever failed to cry;
You’d see the people
That make the weak weaker;
You’d see the monsters
That consume my head;
You’d hear the hollers
That failed to be freed;
You’d see the heart
That still bleeds and bleeds.
If you could read my mind,
You’d see the face
I’ve failed to show back then,
The face I’ve faked back then.
If you could read my mind,
You’d see a character
I had ever failed to become
If you could read my mind,
You’d be able to read
A book you never wished
To touch and read,
But sometimes I still wish
Someone could read my mind.