Topic 3 Schedule - Circular Functions and Trigonometry for IB Mathematics HL Year 1 (Examination 2007)
(A) List of Topics and Content to be Taught
point to consider => some introductory Function concepts have already been presented in Unit 1 Algebra as we graphed and analyzed functions as well as looking at some simple graphing concepts with series and sequences. Of course, most of Unit 2 was about functions. So again in Unit 3, we will also re-visit the graphing and function concepts as in Unit 1 and 2. And again, we study more fundamental algebra skills, this time related to trig and circular fcns.
| Objective | Topic | Content | Teaching Emphasis |
| Objective 3.1 | The Circle | angles in radians | - set stage for angles measured in radians and some physics applications |
| length of arcs | |||
| areas of sectors | |||
| Objective 3.2 | The Unit Circle and Trigonometric Ratios | Definition of sinx, cosx, tanx, secx, cscx, cotx |
- introduce unit circle as an alternate method for looking at trig ratios, apart from the similar triangles and ratio of sides concept |
| Quotient Identity:
tanx = sinx/cosx |
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| Pythagorean Identities: cos2x + sin2x = 1, 1 + tan2x = sec2x, 1 + cot2x = csc2x | |||
| Objective 3.3 | Compound Angle Identities
Double Angle Formulas |
sin(A+B), cos(A+B), tan(A+B) sin(2x), cos(2x), tan(2x) |
- present maybe as simply another identity or see if we can incorporate with Obj. 3.2 |
| Objective 3.4 | Graphs of Circular Functions
The Inverse Trig Functions (arcsin, arccos, arctan) |
graphs of y = sin(x), cos(x), tan(x) | - incorporate unit circle as one way in which we can make sense of the graphs |
| features of the graphs | |||
| transformations/compositions of graphs | |||
| applications of sinusoidal graphs/periodic phenomenon | |||
| Objective 3.5 | Trigonometric Equations | algebraic and graphic solutions of linear trig equations | - can we relate this back to unit circle? Relate to graphs |
| algebraic and graphic solutions of quadratic trig equations | |||
| use of trig identities and factorizations to solve equations | |||
| applications of trig equations => periodic phenomenon | |||
| Objective 3.6 | Solution of Triangles | Sine Law and Applications | |
| Ambiguous Case of Sine Law | |||
| Cosine Law and Applications | |||
| Area of Triangles |
(B) Timing/Pacing
From our list of required content, we can now set up a tentative schedule for Topic 3. Note the recommended time frame is 22 hours (or 16 classes of 1.3333 hours - 80 minutes) (Not enough time really!!!!)
(C) Schedule and Calender
| Apr 24
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Apr 25
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Apr 26
Lesson 84 Chapter 8 Quiz T3.1 - Radians, Sectors, and Arcs |
Apr 27
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Apr 28
Lesson 85 T3.2 - Angles and the Unit Circle (Angles in Standard Position and Their Trig Ratios) |
| May 1
HOLIDAY |
May 2
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May 3
Lesson 86 T3.4 - Graphs of Trigonometric Functions and Their Features |
May 4
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May 5
Lesson 87 T3.4 - Graphs of Transformed Trig Functions
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| May 8
Lesson 88 T3.4 - Inverse Trigonometric Functions - Graphs and Features |
May 9
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May 10
Lesson 89 T3.4 - Modeling with Periodic Functions |
May 11
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May 12
Lesson 90 T3.5 - Trig Identities (Including T3.3 - Compound and Double Angle Formulas) |
| May 15
Lesson 91 T3.5 - Trigonometric Identities |
May 16
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May 17
Lesson 92 T3.5 - Solving Trigonometric Equations |
May 18
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May 19
Lesson 93 T3.5 - Solving Trigonometric Equations |
| May 22
Lesson 94 T3.6 - Solutions of Triangles - Sine and Cosine Laws |
May 23
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May 24
Lesson 95 T3.6 - Sine Law - The Ambiguous Case |
May 25
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May 26
Lesson 96 T3.6 - Applications of Sine Law and Cosine Law |
| May 29
Lesson 97 Binomial Theorem - Review of Combinatorials |
May 30
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May 31
Lesson 98 Binomial Theorem - Binomial Expansions |
June 1
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June 2
Lesson 99 Mathematical Induction |
| June 5
Lesson 100 Mathematical Induction |
June 6
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June 7
Lesson 101 Mathematical Induction |
June 8
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June 9
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