Trigonometry and Measure of Angles

Eddie Woo via YouTube

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Details

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Provider

YouTube
Pricing

Free Video
Languages

English
Duration & workload

9 hours 31 minutes
Sessions

On-Demand
Level

Intermediate

Found in

Master trigonometry fundamentals and advanced concepts through comprehensive video lessons covering angle measurement, trigonometric ratios, and their real-world applications. Explore the basic trigonometric ratios (sine, cosine, tangent) and their reciprocals, understanding why these functions received their names and how they relate to geometric principles. Learn to manipulate trigonometric ratios in geometry problems and discover the importance of trigonometry in mathematics and science. Transition from degree measurement to radian measure, understanding why radians provide a superior system for advanced mathematics and calculus applications. Investigate the unit circle as a foundation for redefining trigonometric functions beyond acute angles, enabling work with obtuse and reflex angles. Develop skills in graphing trigonometric functions, reading values from trigonometric graphs, and understanding the properties of odd and even functions as they relate to trigonometry. Master the Sine Rule and Cosine Rule as powerful extensions of the Pythagorean theorem, including handling the ambiguous case in triangle solving. Apply trigonometric concepts to three-dimensional problems through challenging examples including lighthouse problems and multi-observer scenarios. Calculate arc lengths, sector areas, and segment areas using circular measure formulas. Practice with applied problems ranging from dartboard calculations to wedge measurements, building practical problem-solving skills in trigonometric contexts.

Syllabus

Exact Values for Trigonometric Ratios
Why Degrees?
Why is Trigonometry so important?
Manipulating the Trig Ratios in Geometry (example question)
The Basic Trig Ratios & their Reciprocals
Why are Sine & Cosine given their names?
Redefining the Trig Functions on the Unit Circle (1 of 2: The Basic Concept)
Redefining the Trig Functions on the Unit Circle (2 of 2: Understanding Non-Acute Angles)
How to Graph Trigonometric Functions (1 of 2: Sine)
How to Graph Trigonometric Functions (2 of 2: Cosine & Tangent)
Reading Values from Trigonometric Graphs
Odd & Even Functions (1 of 2: Introductory Examples)
Odd & Even Functions (2 of 2: Relevance to Trigonometry)
Cosine Rule: An Upgrade to Pythagoras' Theorem
Sine Rule: The Ambiguous Case
Why the Sine Rule Works (1 of 3: Acute Angles)
Why the Sine Rule Works (2 of 3: Right Angles)
Why the Sine Rule Works (3 of 3: Obtuse Angles)
3D Trigonometry: a notorious question (1 of 2: Setting up the diagrams)
3D Trigonometry: a notorious question (2 of 2: Working the numbers)
The Lighthouse (Challenging 3D Trig Question)
Introduction to Radians (1 of 3: Thinking about degrees)
Introduction to Radians (2 of 3: Defining a better way)
Introduction to Radians (3 of 3: Definition + Why Radians Aren't Units)
Radian Measure (1 of 4: The worth of Radians in Circles & Calculus)
Radian Measure (2 of 4: Finding ratio between arc length and radius - Why use 'pi'?)
Radian Measure (3 of 4: Finding the formula for the area of a sector in radians)
Radian Measure (4 of 4: Solving Trigonometry with Radians and advantages for calculus)
Circles and Radian Measure (Using Area of Triangle and Sector to find the Area of a Segment)
Trigonometric Functions: Angles of Any Magnitude (1 of 2: The unit circle)
Trigonometric Functions: Angles of Any Magnitude (2 of 2: Obtuse & reflex angles)
Meanings of the Trigonometric Ratios (1 of 4: Re-introducing the Unit Circle)
Meanings of the Trigonometric Ratios (2 of 4: Why is one of them called "tangent"?)
Meanings of the Trigonometric Ratios (3 of 4: Why is one of them called "secant"?)
Meanings of the Trigonometric Ratios (4 of 4: Dynamic visualisation)
Y11 Maths Ext 1 Quiz (3 of 3: Graphs of Trig Functions)
Introduction to Radians (1 of 3: Comparing measurement systems)
Introduction to Radians (2 of 3: Developing an initial sense)
Introduction to Radians (3 of 3: Formal definition & conversion)
Exact Values (1 of 4: Radians vs. Degrees)
Exact Values (2 of 4: Solving a basic trigonometric equation)
Exact Values (3 of 4: Using the unit circle for trigonometry)
Exact Values (4 of 4: Why "tan" is short for "tangent")
Graphs of Basic Trigonometric Functions (1 of 3: Investigating the unit circle with spaghetti)
Graphs of Basic Trigonometric Functions (2 of 3: The features of trigonometric curves)
Graphs of Basic Trigonometric Functions (3 of 3: Graphing examples)
3D Trigonometry Example (1 of 2: Setting up the triangles)
3D Trigonometry Example (2 of 2: Combining the information)
3D Trig Three Observer Problem (1 of 4: Setting up the diagram)
3D Trig Three Observer Problem (2 of 4: Determining ground distances)
3D Trig Three Observer Problem (3 of 4: Calculating ground angles)
3D Trig Three Observer Problem (4 of 4: Resolving the ambiguous case)
Circular Measure: Arc Length, Sector & Segment Area Formulas
Sine Rule - example test question
Cosine Rule - example test question
Dartboard Question (1 of 2: Area)
Dartboard Question (2 of 2: Percentage & perimeter)
Measuring a Wedge
Trigonometry in Right Triangles (5 of 5: Applied problems)
Trigonometry in Right Triangles (4 of 5: Exact values & reciprocals)
Trigonometry in Right Triangles (3 of 5: Finding an angle)
Trigonometry in Right Triangles (2 of 5: Evaluating ratios & angles)
Trigonometry in Right Triangles (1 of 5: Reviewing the ratios)