IIRF Online > Teaching & Academics > Math > Trigonometry > Trigonometry - The Unit Circle, Angles, & Right Triangles
Trigonometry - The Unit Circle, Angles, & Right Triangles by Udemy
Analytical Trig, Verifying Trigonometric Identities, Double Angle Formulas, Inverse Trigonometric Functions & More.
Course Highlights
- Students should have a solid understanding of trigonometry if they work through all of the example problems.
Skills you will learn!
Curriculum
20 Topics
Introduction
Introduction to Angles
Positive and Negative Angles
Acute Angles Right Angles Obtuse Angles and Straight Angles
Angles and Quadrants
Drawing Angles In Standard Position In Degrees
Definition of the Radian
Calculating Radian Measure
Converting Degrees to Radians
Converting Radians to Degrees
Drawing Angles In Standard Position In Radians
Drawing Common Angles In Radian
Coterminal Angles
Converting DMS to Decimal Degrees
Converting Decimal Degrees to DMS
Arc Length
Area of the Sector of a Circle
Linear Speed and Angular Speed Word Problems
Clock Time to Angle Measure
Video Quiz - Angle Measure
9 Topics
Introduction to the Unit Circle
Reference Angles
The Six Trigonometric Functions
Reciprocal Identities
Quotient Identities
Even and Odd Trigonometric Functions
Pythagorean Identities
Periodic Properties
Video Quiz - The Unit Circle
11 Topics
SOH CAH TOA
Finding The Value of the Six Trigonometric Functions
45 45 90 Reference Isosceles Right Triangle
30-60-90 Special Right Triangle
Finding The Value of the Missing Side of a Right Triangle
Finding The Value of the Missing Angle of a Right Triangle
Angle of Elevation vs Angle of Depression
Finding The Height of a Building - Applications of Trigonometry
How To Find The Angle of Elevation
Cofunction Identities
Video Quiz - Right Triangle Trigonometry
7 Topics
Trigonometric Functions of any Angle
The signs of the Trigonometric Functions
Evaluating Trigonometric Functions Given a Point on the Terminal Side
Identifying The Quadrant In Which an Angle Lies
Finding The Exact Value of the Five Remaining Trigonometric Functions
Using Reference Angles to Evaluate Trigonometric Functions
Video Quiz
9 Topics
Introduction to Sine and Cosine Graphs
The Amplitude and Period of a Sine and Cosine Wave
Graphing Trig Functions With a Vertical Shift
Graphing Trigonometric Functions With a Phase shift
Writing The Equation Given The Graph
Sinusoidal Function Word Problem
Graphing Secant and Cosecant Functions
How to Graph Tangent and Cotangent Functions
Video Quiz - Graphing Trigonometric Functions
11 Topics
The Graph of the Inverse Sine Function
Evaluating Inverse Sine Functions
Graphing The Inverse Cosine Function
Finding The Exact Value of the Arc Cosine Function
Graphing The Inverse Tangent Function
Evaluating The Inverse Tan Function
Composition of Inverse Trigonometric Functions
Evaluating a Composition of Different Inverse Trig Functions
Evaluating a Composite Trigonometric Expression
Simplifying Composite Trigonometric Expressions With Inverse Functions
Video Quiz - Inverse Trigonometric Expressions
4 Topics
Solving Two Right Triangle Systems
Introduction to Bearings
Bearing Practice Problems
Video Quiz
9 Topics
Fundamental Identities - List of Formulas & Equations
Converting Into Sine and Cosine
Pythagorean Identities
Factoring
Common Denominators
Splitting Fractions
Multiplying By The Conjugate
Mixed Problems
Video Quiz - Verifying Trigonometric Identities
9 Topics
Sum and Difference Identities
Using The Sum and Difference Formula From Sine
Sum and Difference Formula For Cosine
Find The Exact Value of the Trigonometric Sum and Difference Expression
Sum and Difference Identities With Tangent
Sum and Difference Problems Given Sine Alpha and Beta
Verifying Trigonometric Identities With Sum and Difference Formulas
Simplifying Inverse Trigonometric Functions With Sum and Difference Identities
Video Quiz - Sum and Difference Identities
12 Topics
Double Angle Formulas
Using Double Angle Formulas to Find Exact Values
Alternative Double Angle Problems
Verifying Trigonometric Identities With Double Angle Formulas
Power Reducing Formulas
Using The Power Reducing Formulas To Simplify Trigonometric Expressions
Half Angle Identities
Using Half Angle Formulas to Find The Exact Value
Right Triangle Trigonometry and Half Angle Identities
Verifying Trigonometric Identities With Half Angle Formulas
Inverse Trig Functions With Double Angle Formulas and Half Angle Identities
Video Quiz - Double Angle Formulas & Half Angle Identities
5 Topics
Product To Sum Formulas
Using The Product-To-Sum Formulas To Simplify Trigonometric Expressions
Sum To Product Formulas
Using The Sum-To-Product Formulas To Simplify Trigonometric Expressions
Verifying Trigonometric Identities Using Sum-To-Product Formulas
6 Topics
Solving Trigonometric Equations By Finding All Solutions
Beware of This
Solving Trigonometric Equations With Multiple Angles
Solving Trigonometric Equations By Factoring
Solving Trigonometric Equations Using Identities
Video Quiz - Solving Trigonometric Equations
10 Topics
Introduction to the Law of Sines
Law of Sines Example - AAS
Law of Sines Example - SSA One Solution
Law of Sines Example - SSA No Solution
SSA - Two Solutions
Area of an Oblique Triangle
Law of Cosines SAS - Finding The Missing Side
Law of Cosines SSS - Finding The Missing Angle Measure
Area of a SSS Triangle - Heron's Formula
Video Quiz - Law of Sines and Cosines
8 Topics
Introduction to Polar Coordinates
Plotting Points in a Polar Coordinate System
Finding Other Polar Coordinates for a Given Point
Polar Coordinates to Rectangular Coordinates Point Conversion
Rectangular Coordinates to Polar Coordinates
Polar Equations to Rectangular Equations
Rectangular Equations to Polar Equations
Video Quiz - Polar Coordinates
6 Topics
Graphing Circles Using Sine and Cosine Functions
Graphing Limacons Part 1
Graphing Limacons Part 2
Graphing Rose Curves Part 1
Graphing Rose Curves Part 2
Graphing Lemniscates
10 Topics
Plotting Complex Numbers
Finding The Absolute Value of a Complex Number
Converting Complex Numbers From Rectangular Form to Polar Form
Polar Form to Rectangular Form
Products of Complex Numbers
Quotients of Complex Numbers
Powers of Complex Numbers
Roots of a Complex Number
Cube Root of a Number
Solving Equations With Complex Numbers
12 Topics
Scalar and Vector Quantities
Representing a Vector in Rectangular Coordinates
Finding The Terminal Point Given The Initial Point & Vector
Finding The Initial Point
The i j and k Vectors in Rectangular Coordinates
Finding The Magnitude and Direction
Scalar Multiplication of Vectors
Adding and Subtracting Vectors
Writing a Vector in Terms of its Magnitude and Direction
Unit Vectors
Adding Vectors Graphically
Adding Vectors Using Component Methods
7 Topics
Dot Product of Two Vectors
Properties of the Dot Product
Finding The Magnitude of a Vector
Finding The Dot Product of Two Vectors Given The Magnitude and Angle
The Angle Between Two Vectors
Parallel Orthogonal or Neither?
Writing Vectors In Component Form
Trigonometry - The Unit Circle, Angles, & Right Triangles
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