City of Angels School Student



City of Angels School

Independent Study

Los Angeles Unified School District

Course Title: Math Analysis / Trigonometry B

Student’s Instructional Guide

Text: Larson, Hostetler, and Edwards, Precalculus with Limits, 5th ed., Brooks-Cole/Cengage Learning, 2008

Prerequisite: Grade of “C” or better in Math Analysis A

Student ________________________

Teacher ________________________

Beginning Date _______________

Ending Date ___________________

Final Mark _______ Credits _5_

Course Description

The purpose of this course is to develop a firm background in, and to extend the understanding of pre-calculus topics and concepts. This discipline combines many of the trigonometric, geometric, and algebraic techniques needed to prepare students for the study of calculus. The most significant new concept is that of limits. Math Analysis AB meets the UC/CSU admission requirement C.

Content

Material covered in this course is in line with California state content standards for mathematics.

Websites



The Khan Academy is a not-for-profit educational organization created by Salman Khan. With the stated mission "of providing a high quality education to anyone, anywhere", the Academy supplies a free online collection of just under 2,000 videos on mathematics, history, finance, physics, chemistry, astronomy, and economics. Recently featured on CNN, ABC, and the PBS Newshour. No password is required.



This site walks students through a step-by-step solution for every odd-numbered problem in their textbook. Login password: angels123

Homework

• Students should expect to work two hours a day, five days a week on assignments for this course.

• Label your homework with student name, chapter and section number.

• Please write down the problem, show all necessary work and check your answers using the answer key at the back of the book.

• Remember that all Quizzes, Chapter Tests, and Periodic Assessments will be taken at the site.

Grades

Final grades will be based on the following matrix:

|Homework |40% |

|Chapter Tests |30% |

|Final Exam |10% |

Weekly Assignments will be graded based on the following standard breakdown for work complete/correct:

|A |90-100% |

|B |80-89% |

|C |70-79% |

|D |60-69% |

|F |0-59% |

|Assignment for Week # 1 |Date Assigned |Date Due |

|Chapter 4: Trigonometric Functions | | |

|(Sections 4.1 – 4.2) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|4.1 Radian and Degree Measure |Radian and Degree Measure |(4) |

| | | |

|Study Examples 1-7. | |Radian and Degree Measure 35:51 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 265-268, Exercises # 3-87 (every other odd), 96, 97 | | |

| | | |

|4.2 Trigonometric Functions: The Unit Circle |Trig Function - Unit Circle |(4) |

| | | |

|Study Examples 1-4. |Unit Circle |Trigonometric Functions: The Unit |

|View any or all of the videos to the right. | |Circle 28:07 |

|Homework: pgs. 274-275, Exercises # 1-29 (every other odd), 31, 35, 39, 43, 45, | | |

|47, 51-67 (odd) | | |

|Assignment for Week # 2 |Date Assigned |Date Due |

|Chapter 4: Trigonometric Functions | | |

|(Sections 4.3 – 4.4) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|4.3 Right Triangle Trigonometry |Trig Identities 1 |(4) |

| | | |

|Study Examples 1-9. |Trig Identity - Proof |Right Triangle Trigonometry 42:02 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 284-287, Exercises # 3, 9, 11, 17-47 (odd), 55, 57, 59, 69, 73, | | |

|77, 81, 82 | | |

| | | |

|4.4 Trigonometric Functions of Any Angle | |(4) |

| | | |

|Study Examples 1-7. | |Trigonometric Functions of Any |

|View any or all of the videos to the right. | |Angle 55:50 |

|Homework: pgs. 294-296, Exercises # 1-105 (every other odd) | | |

| | | |

|Study for Unit Circle Test | | |

|Assignment for Week # 3 |Date Assigned |Date Due |

|Chapter 4: Trigonometric Functions | | |

|(Sections 4.5 – 4.6) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|4.5 Graphs of Sine and Cosine Functions |Graph of Sine |(4) |

| | | |

|Study Examples 1-8. |Amplitude for sine and cosine function|Graphs of Sine and Cosine Functions|

|View any or all of the videos to the right. | |50:48 |

|Homework: pgs. 304-305, Exercises # 1-21 (every other odd), 29, 31, 39, 40, | | |

|41-59 (odd), 65 | | |

| | | |

|4.6 Graphs of Other Trigonometric Functions |Trig Graph |(4) |

| | | |

|Study Examples 1-6. | |Graphs of Other Trigonometric |

|View any or all of the videos to the right. | |Functions 67:06 |

|Homework: pg. 316, Exercises # 5-29 (odd) | | |

|Assignment for Week # 4 |Date Assigned |Date Due |

|Chapter 4: Trigonometric Functions | | |

|(Sections 4.7 – 4.8) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|4.7 Inverse Trigonometric Functions |Inverse Arcsine |(4) |

| | | |

|Study Examples 1-7. |Inverse Arccosine |Inverse Trigonometric Functions |

|View any or all of the videos to the right. | |42:28 |

|Homework: pgs. 327-328, Exercises # 1- 9 (odd), 10, 15-61 (odd) |Inverse Arctan | |

| | | |

|4.8 Applications and Models |Harmonic Motion 1 |(4) |

| | | |

|Study Examples 1-7. |Harmonic Motion 2 |Applications and Models 24:32 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 337-341, Exercises # 1, 5, 9, 13, 17, 21, 27, 33, 51, 55 | | |

| | | |

|Study for Chapter 4 Test | | |

|Assignment for Week # 5 |Date Assigned |Date Due |

|Chapter 5: Analytic Trigonometry | | |

|(Sections 5.1 – 5.3) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|5.1 Using Fundamental Identities |Identities |(5) |

| | | |

|Study Examples 1-9. |Identities 2 |Using Fundamental Identities 30:16 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 357-359, Exercises # 3, 7, 11, 27-71 (odd), 81, 83 | | |

| | | |

|5.2 Verifying Trigonometric Identities | |(5) |

| | | |

|Study Examples 1-7. | |Verifying Trigonometric Identities |

|View any or all of the videos to the right. | |20:02 |

|Homework: pgs. 365-367, Exercises # 1-9 (odd), 21-49 (odd), 63, 65 | | |

| | | |

|5.3 Solving Trigonometric Equations | |(5) |

| | | |

|Study Examples 1-12. | |Solving Trigonometric Equations |

|View any or all of the videos to the right. | |54:04 |

|Homework: pgs. 376-377, Exercises # 7-53 (odd), 61- 71 (odd) | | |

|Assignment for Week # 6 |Date Assigned |Date Due |

|Chapter 5: Analytic Trigonometry | | |

|(Sections 5.4 – 5.5) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|5.4 Sum and Difference Formulas |Sine |(5) |

| | | |

|Study Examples 1-8. |Cosine |Sum and Difference Formulas 22:32 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 384-385, Exercises # 1-21 (odd), 35-71 (every other odd) | | |

| | | |

|5.5 Multiple-Angle and Product-to-Sum Formulas |Identity 3 |(5) |

| | | |

|Study Examples 1-11. | |Multiple-Angle and Product-to-Sum |

|View any or all of the videos to the right. | |Formulas 38:31 |

|Homework: pgs. 394-396, Exercises # 3, 7, 13-25 (odd), 39, 43, 47, 51, 57, 63, | | |

|81, 85, 93-99 (odd), 105 | | |

| | | |

|Study for Chapter 5 Test | | |

|Assignment for Week # 7s O |Date Assigned |Date Due |

|Chapter 6: Additional Topics in Trigonometry | | |

|(Sections 6.1 – 6.2) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|6.1 Law of Sines |Law of Sines |(6) |

| | | |

|Study Examples 1-7. | |Law of Sines 27:27 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 414-415, Exercises # 1-27 (odd) | | |

| | | |

|6.2 Law of Cosines |Law of Cosines |(6) |

| | | |

|Study Examples 1-5. |Heron's Formula |Law of Cosines 16:37 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 421-422, Exercises # 1, 5, 9, 11, 13, 27, 29, 37, 39, 45 | | |

|Assignment for Week # 8 |Date Assigned |Date Due |

|Chapter 6: Additional Topics in Trigonometry | | |

|(Sections 6.3 – 6.5) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|6.3 Vectors in a Plane |Unit Vector Notation |(6) |

| | | |

|Study Examples 1-10. |Unit Vector 2 |Vectors in a Plane 58:25 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 433-436, Exercises # 1, 5, 25, 37, 51, 57, 65, 83, 85, 89 |Vector - Plane | |

| | | |

|6.4 Vectors and Dot Products |Dot Products |(6) |

| | | |

|Study Examples 1-8. | |Vectors and Dot Products 39:39 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 445-447, Exercises # 1, 9, 11, 17, 35, 45, 61, 63 | | |

| | | |

|6.5 Trigonometric Form of a Complex Number |Root of Complex Number |(6) |

| | | |

|Study Examples 1-8. |Complex Number 2 |Trigonometric Form of a Complex |

|View any or all of the videos to the right. | |Number |

|Homework: pgs. 456-459, Exercises # 5, 19, 37, 55, 61, 91, 135, 139 | | |

| | | |

|Study for Chapter 6 Test | | |

|Assignment for Week # 9 |Date Assigned |Date Due |

|Chapter 9: Topics in Analytic Geometry | | |

|(Sections 9.1 – 9.3) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|9.1 Circles and Parabolas |Conic Section |(9) |

| | | |

|Study Examples 1-7. |Identifying Conic Section |Circles and Parabolas 47:20 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 667-668, Exercises # 1-11 (odd), 23, 25, 29, 31, 45, 49, 53, |Circle | |

|59-65 (odd), 77, 79, 81, 85, 87 | | |

| |Identifying Parabolas | |

| | | |

| |Parabola ( Focus ) | |

| | | |

|9.2 Ellipses |Ellipses |(9) |

| | | |

|Study Examples 1-5. |Foci |Ellipses 39:34 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 677-678, Exercises # 7-37 (odd) | | |

| | | |

|9.3 Hyperbolas |Hyperbolas (Intro) |(9) |

| | | |

|Study Examples 1-7. |Hyperbolas 2 |Hyperbolas 42:10 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 687-689, Exercises # 5-41 (odd), 49-57 (odd) |Foci | |

| | | |

|Study for Chapter 9 Test | | |

|Assignment for Week # 10 |Date Assigned |Date Due |

|Chapter 11: Limits and an Introduction to Calculus | | |

|(Sections 11.1 – 11.3) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|11.1 Introduction to Limits |Intro to Limit |(11) |

| | | |

|Study Examples 1-10. |Intro to Limit 2 |Introduction to Limits 22:17 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 788-790, Exercises # 1, 3, 5, 11, 25, 31, 32, 33, 47-69 (odd) | | |

| | | |

|11.2 Techniques for Evaluating Limits |Evaluating Limit |(11) |

| | | |

|Study Examples 1-9. | |Techniques for Evaluating Limits |

|View any or all of the videos to the right. | |17:55 |

|Homework: pgs. 798-799, Exercises # 1-27 (odd), 53-59 (odd), 69-75 (odd) | | |

| | | |

|11.4 Limits at Infinity and Limits of Sequences |Limits with Infinity |(11) |

| | | |

|Study Examples 1-5. | |Limits at Infinity and Limits of |

|View any or all of the videos to the right. | |Sequences 20:39 |

|Homework: pgs. 817-818, Exercises # 9-27 (odd), 39, 49 | | |

| | | |

|Study for Chapter 11 Test | | |

|Assignment for Week # 11 |Date Assigned |Date Due |

|Study for Final Exam | | |

| | | |

| | | |

|Complete the Final Exam for Math Analysis B. | | |

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