Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
Algebra II / E&I Algebra
Exponents & Polynomials Intermediate Algebra starts here!

Factoring Rational Expressions Rational Equations and Applications
Algebra III / Inter. Algebra
Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
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Calculus III
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
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Course: Trigonometry
Topic: Circular Functions
Subtopic: Arc Length & Area of a Sector

Overview

This lesson is dedicated to two important circle formulas, the length of an arc of a circle (s=rθ) and the area of a sector of a disk (A=½r2θ). These will enable us to extend our ability to solve application problems.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 3.4.1 Use the arc length formula to find s, r, or theta.
• 3.4.2 Use the area of a sector formula to find A, r, or theta
• 3.4.3 Realize that theta in both of the above formulae is in radian measure only

Terminology

Define: arc, circle vs. disk, central angle, subtends, arc length, sector of a disk

Supplementary Resources (recommended)

READ THIS ARTICLE Radian Angular Measure which is an excerpt from Trigonometric Delights by Eli Maor, Princeton University Press, 1998. The article answers such questions as, "Why are there 360 degrees in a circle?", "Why are angles measured counterclockwise?", and "Why use radians over degrees?". Math majors are definitely encouraged to read the entire book (and everything else my Eli Maor, in my opinion).

Supplemental Resources (optional)