# Trigonometry and Analytic Geometry (MATH 133 A)

## Fall 2013

Instructor:   Dr. Seongchun (Michelle) Kwon
e-mail:   kwonseon at hotmail dot com
Office:
Office hours:   or by appointment
Class hours:   2:30 PM-3:50 PM Thursday, 102 Miller Hall

Text:

Materials covered:    Right triangle ratios, trigonometric functions, graphing trigonometric functions, identities, inverse trigonometric functions, laws of Sines and Cosines, polar coordinates and complex numbers, analytic geometry.

Final Comprehensive Exam:   December 5

• Syllabus
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## Schedule

 Week Days Your Progress 1 Aug 27 - Sep 1 Introduction, 1.1. Radian and Degree Measure 2 Sep 2 - Sep 8 1.2. Trigonometric Functions: The Unit Circle, 1.3. Right Triangle Trigonometry 3 Sep 9 - Sep 15 1.4. Trigonometric Functions of Any Angle, 1.5. Graphs of Sine and Cosine Functions 4 Sep 16 - Sep 22 1.6. Graphs of Other Trigonometric Functions, 1.7. Inverse Trigonometric Functions 5 Sep 23 - Sep 29 1.7. Inverse Trigonometric Functions, 2.1. Using Fundamental Identities 6 Sep 30 - Oct 6 Review for the Exam, Exam 1(1.1-2.1) 7 Oct 7 - Oct 13 2.2. Verifying Trigonometric Identities, 2.3. Solving Trigonometric Equations 8 Oct 14 - Oct 20 2.3. Solving Trigonometric Equations, 2.4. Sum and Difference Formulas 9 Oct 21 - Oct 27 2.5. Multiple-Angle and Product-to-Sum Formulas, 3.1. Law of Sines 10 Oct 28 - Nov 3 3.2. Law of Cosines, Review for the Exam 2 11 Nov 4 - Nov 10 Exam 2(2.2-3.2), 3.3. Vectors in the Plane 12 Nov 11 - Nov 17 3.4. Vectors and Dot Products, 4.1. Complex Numbers 13 Nov 18 - Nov 24 4.2. Complex Solutions of Equations, 4.3. Trigonometric Form of a Complex Number 14 Nov 25 - Dec 1 4.4. DeMoivre's Theorem, 6.6. Parametric Equations 15 Dec 2 - Dec 8 6.7. Polar Coordinates, Exam 3 16 Dec 9 - Dec 13 Final Exam

## Lecture Note, Video Resources

Most video lectures are taken from either ProfRobBob(R) or mathispower4u(J).
I thank to Mr.Tarrou and Prof. Sousa for their willingness to share their high quality lectures for this hybrid course.

 Topic, Powerpoint Lecture Note ( Partly based on the Powerpoint provided by Cengage Learning ) Video Lectures, Recourses 1.1. Radian and Degree Measure 1.2. Trigonometric Functions: The Unit Circle The Unit Circle Definition of Trig Functions(R); 1.3. Right Triangle Trigonometry Right Triangle Trigonometry(R) ; Degrees, Minutes and Seconds(J) 1.4. Trigonometric Functions of Any Angle Determining Trig Function Values Using Reference Angles and Reference Triangles(J) 1.5. Graphs of Sine and Cosine Functions Understanding Basic Sine & Cosine Graphs(R); Amplitude and Period of Sine and Cosine(J); Graphing Sine and Cosine with Transformations(J) 1.6. Graphs of Other Trigonometric Functions 1.7. Inverse Trigonometric Functions Introduction to Inverse Sine, Inverse Cosine, and Inverse Tangent(J); Evaluating Inverse Trigonometric Functions Full Length(R) 2.1. Using Fundamental Identities The Reciprocal, Quotient, and Pythagorean Identities(J) ; Fundamental Trigonometric Identities: Reciprocal, Quotient, and Pythagorean Identities(J); Verifying Trig Identities(Part1)(R) 2.2. Verifying Trigonometric Identities Verifying Trigonometric Identities (Part2)(R) Verifying Trigonometric Identities (Part3)(R) 2.3. Solving Trigonometric Equations Trigonometric Equations Single Angle 0 to 2pi Restriction(R) Single Angle Trigonometric Equations All Solutions(R) Trigonometric Equations Multiple Angles 0 to 2pi Restriction(R) 2.4. Sum and Difference Formulas Sum and Difference Trigonometric Identities(R) 2.5. Multiple-Angle and Product-to-Sum Formulas Double Angle Identities (J) Power Reducing Formulas for Sine and Cosine, Example 1 (P) Half Angle Identities (J) 3.1. Law of Sines Oblique Triangles Law of Sines (R) Ambiguous Case for Law of Sines (R) 3.2. Law of Cosines Law of Cosines (R) Area of oblique triangles with Heron's Formula (R) Applications of Law of Sines and Cosines (R) 3.3. Vectors in the Plane Introduction to Vectors(J) Vector Operations(J): Watch up to 4:59 The Unit Vector(J) 3.4. Vectors and Dot Products Dot Product & Angle Between Vectors(R) Projection of a Vector onto another Vector(R) Vector Application Examples(R): Watch up to 7:00 minutes 4.1. Complex Numbers Complex Numbers.(R) 4.2. Complex Solutions of Equations(:) Complex (imaginary) Numbers Part 2(R) Polynomial Function - Complex Factorization Theorem(J) Finding polynomials using the Linear Factorization Theorem(R) 4.3. Trigonometric Form of a Complex Number Complex Numbers in Polar Form(R) Product & Quotient of Polar Complex Numbers(R) 4.4. DeMoivre's Theorem Precise Version (R); Shorter Version (J) De Moivre's Theorem Roots of Polar Complex Numbers(R) 6.6. Parametric Equations Introduction to Parametric Equations(R) Parametric Equations Eliminating Parameter T(R) 6.7. Polar Coordinates Understanding Polar Coordinates(R) Converting Coordinates between Polar and Rectangular Form(R) Converting Polar Equations to Rectangular Equations(J) 