# Trigonometry and Analytic Geometry

## Multi-Media Resources

Instructor:   Dr. Seongchun (Michelle) Kwon
e-mail:   kwonseon at hotmail dot com

## 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)