MATH 1201 - Trigonometry

Video Examples of Concepts

Created by Bruce Bordwell and Candace Blazek

Anoka-Ramsey Community College Mathematics Department

Polynomials

• Long Division
• Synthetic Division
• Remainder Theorem
• Rational Zero Theorem
• Solving a Polynomial Equation
• Finding all Zeros of a polynomial function

Conic Sections

• Writing the standard form of an ellipse and graphing
• Finding the standard equation of graphed ellipse
• Graphing a hyperbola from a standard form equation
• Writing the standard equation of a parabola and graphing

Rational Functions

• Finding a Slant Asymptote

Parametric Equations

• Graphing a Parametric Equation
• Eliminating the parameter to graph a parametric equation
• Defining Parametric Equations for y = f(x) *Calculator

Angles Degrees and Radian Measure

• Converting between decimal and degrees-minutes-seconds of an angle *Calculator
• Arc Lengh
• Coterminal Angles

Trig Functions

• Finding Values of the 6 Trig Functions
• 30-60-90 Triangle
• Using a Reference Triangle
• Finding Reference Angles
• Using Reference Angles
• Trig Functions of Real Values 1 - using the unit circle
• Trig Functions of Real Values 2 - using the unit circle

Graphing Trig Functions

• Graphing the Function y = 1/2 sin 3x
• Graphing the Function y = -2 cos (3x + π)
• Graphing the Function y = csc 2x
• Graphing the Function y = -tan 3x *Calculator

Inverse Trig Functions

• Finding the Inverse Sine Exactly *Calculator
• Finding the Inverse Cosine Exactly *Calculator
• Finding the Inverse Tangent Exactly *Calculator
• Evaluating a Composite Trig Expression  - finding the exact value
• Evaluating a Composite Trig Expression  - finding the algebraic expression

Applications of Trig Functions

• Distance Across Lake *Calculator
• Angle of Elevation *Calculator
• Finding the Height of a Tree
• Involving Bearing
• Ascending Balloon - Using Two Right Triangles to Solve a Problem
• Simple Harmonic Motion - Displacement, Period and Frequency

Induction

• Finding statement when n=k and n=k+1
• Proof Example

Verifying Identities

• Examples Using Fundamental Trigonometric Identities

Sum and Difference Formulas for Sine, Cosine, and Tangent

• Examples Using Sum and Difference Formulas

Product to Sum  & Sum to Product Formulas

• Product to Sum Examples
• Sum to Product Examples

Half Angle Formulas and Double Angle Formulas

• Half-Angle Formula Examples
• Double-Angle Formula Examples

Trigonometric Equations

• Examples.

Law of Sines

• Solving Triangles Ex 1
• Solving Triangles Ex 2
• Example of Application

Law of Cosines

• Examples of Solving Triangles
• Examples of Applications

Matrices

• Solving Linear System of Equations Using Augmented Matrices, Adding Matrices, Multiplying Matrices