About This Chapter
Who's it for?
This unit of our High School Trigonometry Homeschool Curriculum course will benefit any student who is trying to learn about circular arcs, circles and angles. There is no faster or easier way to learn about circular arcs, circles and angles. Among those who would benefit are:
- Students who require an efficient, self-paced course of study to learn how to measure angles, arcs and circles.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need a math curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.
How it works:
- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and a Circular Arcs, Circles and Angles unit exam confirm understanding or identify any topics that require review.
Circular Arcs, Circles and Angles Unit Objectives:
- Measure the area and circumference of a circle.
- Measure an inscribed angle.
- Find the arc length of a sector.
- Measure angles and lengths formed by chords, secants and tangents.
- Identify the parts of a regular polygon.
1. Circles: Area and Circumference
Understanding how to calculate the area and circumference of circles plays a vital role in some of our everyday functions. In this lesson, learn how to find the area and circumference of circles by working through several examples.
2. Inscribed and Circumscribed Figures: Definition & Construction
A square and a circle may be different shapes, but they still can have a unique relationship. In this lesson, we'll learn about inscribed and circumscribed figures.
3. How to Find the Measure of an Inscribed Angle
Finding the measure of an inscribed angle requires knowing a little information. In this lesson, we'll find the measure of an inscribed angle when we know the measure of the central angle or one or more of the arcs formed by the angle.
4. Tangent of a Circle: Definition & Theorems
What happens when a line just barely touches a circle? It's a tangent! In this lesson, we'll learn all about tangents to circles, including a few key theorems. We'll also look at tangent circles.
5. Arc Length of a Sector: Definition and Area
In this lesson, we'll slice up a circle like it's a pizza and learn how to find out useful information about our slices. We'll find out the area of these sectors, or pie slices. We'll also learn about arc lengths.
6. Measurements of Angles Involving Tangents, Chords & Secants
When lines and circles meet, angles are formed. Fortunately, we can determine the measure of these angles, whether they're formed by tangents, secants or chords, just by knowing the measure of the created arcs.
7. Measurements of Lengths Involving Tangents, Chords and Secants
The lengths of chords, tangents and secants take on unique relationships when they're drawn on circles. In this lesson, we'll define those relationships and see them in action.
8. Regular Polygons: Definition & Parts
What makes a polygon a polygon? And what shapes are considered polygons? In this lesson, find out the answers to these questions and more as we learn all about polygons and their parts.
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Other chapters within the High School Trigonometry: Homeschool Curriculum course
- Types of Real Numbers: Homeschool Curriculum
- Working with Linear Equations: Homeschool Curriculum
- Graphing Inequalities: Homeschool Curriculum
- Absolute Value Equations: Homeschool Curriculum
- Complex Numbers: Homeschool Curriculum
- Using Systems of Linear Equations: Homeschool Curriculum
- Mathematical Modeling: Homeschool Curriculum
- Introduction to Quadratics: Homeschool Curriculum
- Quadratic Functions: Homeschool Curriculum
- Coordinate Geometry: Homeschool Curriculum
- Functions for Trigonometry: Homeschool Curriculum
- Function Operations: Homeschool Curriculum
- Graph Symmetry: Homeschool Curriculum
- Graphing with Functions: Homeschool Curriculum
- Polynomial Functions Basics: Homeschool Curriculum
- Higher-Degree Polynomial Functions: Homeschool Curriculum
- Difference Quotients: Homeschool Curriculum
- Function Graphs: Homeschool Curriculum
- Exponential Functions: Homeschool Curriculum
- Trigonometric Functions: Homeschool Curriculum
- Triangle Trigonometry: Homeschool Curriculum
- Trigonometric Graphs: Homeschool Curriculum
- Solving Trigonometric Equations: Homeschool Curriculum
- Trigonometric Identities: Homeschool Curriculum
- Trigonometric Applications: Homeschool Curriculum
- Analytic Geometry: Homeschool Curriculum
- Vectors, Matrices & Determinants: Homeschool Curriculum
- Polar Coordinates: Homeschool Curriculum