Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / 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
Precalculus II / 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
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

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 = r theta) and the area of a sector of a disk (A = 1/2 r^2 theta). 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

Terms you should be able to define: arc, circle vs. disk, central angle, subtends, arc length, sector of a disk

Mini-Lectures and Examples

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)

rev. 2020-10-10