Trigonometry
912
Course Outline
This course will focus on the study of angles; the trigonometry of angles and real numbers; the trigonometric functions and their inverses including their graphs; solutions of right and oblique triangles; verification of fundamental identities and analytic trigonometry; addition, subtraction and multiple angle formulas; the laws of sines and cosines; vectors and the dot and cross product; complex numbers, De Moivre’s Theorem and nth roots of complex numbers; polar coordinates and equations. The course will also include the study of functions including exponential and logarithmic functions.
TRIGONOMETRIC FUNCTIONS

Extend the domain of trigonometric functions using the unit circle

Model periodic phenomena with trigonometric functions

Prove and apply trigonometric identities
THE COMPLEX NUMBER SYSTEM

Perform arithmetic operations with complex numbers

Represent complex numbers and their operations on the complex plane

Use complex numbers in polynomial identies and equations
VECTOR & MATRIX QUANTITIES

Represent and model with vector quantities

Perform operations on vectors
SIMILARITY, RIGHT TRIANGLES TRIGONOMETRY

Define trigonometric ratios and solve problems involving right triangles

Apply trigonometry to general triangles

Angles & Triangles
Angles and Angle Measures:

Handout: Angles & Angle Measures Worksheet

Assignment: Angles & Angle Measures

Worksheet: Converting Angle Measures
Triangle Review:

Handout: Triangle Review Worksheet

Assignment: Triangle Review
Pythagorean Theorem:

Handout: Pythagorean Theorem Worksheet

Assignment: Pythagorean Theorem
Special Right Triangles:

Handout: Special Right Triangles Worksheet

Assignment: Special Right Triangles
Basic Trigonometric Ratios:

Handout: Basic Trigonometric Ratios Worksheet

Assignment: Basic Trigonometric Ratios
Inverse Trigonometric Ratios:

Worksheet: Inverse Trigonometric Ratios
Laws of Sine & Cosine:

Handout: Law of Sines & Cosines Worksheet

Assignment: Law of Sines & Cosines
The Unit Circle:

Handout: Unit Circle

Handout: Finding Trig Values

Handout: Evaluating Trig Functions Worksheet

Assignment: Evaluating Trig Functions

Graphs of Trigonometric Functions
Graphs of Sine & Cosine:

Handout: Graphs of Sine & Cosine Worksheet

Assignment: Graphs of Sine & Cosine
Linear & Angular Velocity:

Handout: Linear & Angular Velocity Worksheet

Assignment: Linear & Angular Velocity
Graphs of Other Trig Functions:

Handout: Cotangent Graph Exploration

Assignment: Cotangent Graph Exploration
Translations of Trig Functions:

Handout: Translations of Trig Functions Worksheet

Assignment: Translations of Trig Functions
Applications of Trig Functions:

Handout: Sinusoidal Applications Worksheet

Essay: RealWorld Applications

Assignment: Sinusoidal Applications

Trigonometric Identities
Fundamental Trigonometric Identities:

Handout: Fundamental Trigonometric Identities Worksheet

Assignment: Fundamental Trigonometric Identities
Proving Trigonometric Identities:

Handout: Proving Trig Identities Worksheet

Assignment: Proving Trig Identities
Sum & Difference Identities:

Handout: Sum & Difference Identities Worksheet

Assignment: Sum & Difference Identities

Essay: Sum & Difference Identities Short Answer
DoubleAngle & HalfAngle Identities:

Handout: Double & HalfAngle Identities Worksheet

Assignment: Double & HalfAngle Identities

Essay: Double & HalfAngle Identities Short Answer
Solving Trigonometric Equations:

Handout: Solving Trig Equations Worksheet

Assignment: Solving Trig Equations

MidTerm Exam

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Assignment: Midtest

Handout: Trigonometry MidTerm Exam

Assignment: Trigonometry MidTerm Exam

Inverse Trig Functions
Review: Basic Inverse Trig Functions:

Handout: Inverse Review Worksheet

Assignment: Inverse Review
Graphs of Inverse Trig Functions:

Handout: Inverse Trig Graphs Worksheet

Assignment: Inverse Trig Graphs
Inverse Trig Properties:

Handout: Inverse Trig Properties Worksheet

Assignment: Inverse Trig Properties
Area of Triangles:

Handout: Area of Triangles Worksheet

Assignment: Area of Triangles

Vectors
Introduction to Vectors:

Handout: Introduction to Vectors Worksheet

Assignment: Introduction to Vectors
Geometric Vectors: Adding & Subtracting:

Handout: Geometric Vectors

Assignment: Geometric Vectors
Algebraic Vectors:

Handout: Algebraic Vectors Worksheet

Assignment: Algebraic Vectors

The Polar System
Polar Coordinates:

Handout: Polar Coordinates Worksheet

Assignment: Polar Coordinates
Graphing Polar Equations:

Handout: Graphing Polar Equations Worksheet

Assignment: Graphing Polar Equations
Polar & Rectangular Coordinates:

Handout: Converting Polar & Rectangular Equations Worksheet

Worksheet: Converting Polar & Rectangular Coordinates

Assignment: Converting Polar & Rectangular Equations
Complex Numbers:

Handout: Operations With Complex Numbers Worksheet

Assignment: Operations With Complex Numbers
Polar Form of Complex Numbers:

Handout: Polar Form of Complex Numbers Worksheet

Assignment: Polar Form of Complex Numbers
Complex Numbers in Polar Form: Products & Quotients:

Handout: Products & Quotients Worksheet

Assignment: Products & Quotients
De Moivre’s Theorem:

Handout: De Moivre’s Theorem Worksheet

Assignment: De Moivre’s Theorem

Final Exam
PostTest:

Assignment: PostTest

Handout: Trigonometry Final Exam

Assignment: Final Exam