Handout
Purple Math

Purplemath: Sectors, Areas, and Arcs

For Students 6th - 8th Standards
Explains formulas for areas of sectors of circles and lengths of arcs. Demonstrates how to use the formulas in each of degrees and radians.
Activity
Paul Dawkins

Paul's Online Notes: Calculus Ii: Parametric Equations and Polar Coordinates

For Students 9th - 10th
The resource examines parametric equations and polar coordinates. Topics investigated are parametric curves, area with parametric equations, arc length with polar coordinates, and surface area with polar coordinates. Class notes,...
Unit Plan
CK-12 Foundation

Ck 12: Trigonometry: Length of an Arc

For Students 10th - 12th
[Free Registration/Login may be required to access all resource tools.] Definition and measurement of an arc on a circle,
Handout
CK-12 Foundation

Ck 12: Geometry: Circles: Segments and Lengths Study Guide

For Students 9th - 10th Standards
This study guide on circles covers some vocabulary and theorems about segments and lengths. It is available for download with free registration.
Activity
Texas Instruments

Texas Instruments: Math Today Coming Clean About Showering Time

For Teachers 9th - 10th
In this activity using the USA TODAY Snapshot, "Coming clean about showering time," students will find the measures of central angles and arcs of a circle. They will use circumference, radius, concentric circles and degrees in a circle...
Activity
Other

Old Dominion University: Calculus Animations W Mathcad

For Students 9th - 10th
Explanations and animations of limits, slopes, derivatives, arc length, infinite series, conic sections, cycloids, parametric curves, polar curves, quadric surfaces, and more.
Handout
Paul Dawkins

Paul's Online Notes: Calculus Ii: Applications of Integrals

For Students 9th - 10th
The resource examines applications of integration. Topics investigated are arc length, surface area, center of mass, hydrostatic pressure, and probability density functions. Class notes, definitions, and examples with detailed solutions...
Graphic
Math2

Math2: Circles

For Students 9th - 10th Standards
This site has many useful formulas and examples relating to circles, including related definitions, circumference of a circle, area of a circle, length of a circular arc, area of a circular sector, equation of a circle in cartesian...
Unit Plan
Cuemath

Cuemath: Circles

For Students 3rd - 8th Standards
Explore everything about circles. Learn various parts of a circle like a diameter, radius, circumference, circles chord, tangent circles, major arc, segment, sector, and discover other interesting aspects of it. Try your hand at solving...
Lesson Plan
Illustrative Mathematics

Illustrative Mathematics: F Tf.1 What Exactly Is a Radian?

For Teachers 9th - 10th Standards
For this task, students use a piece of string or another tool to measure the radius of the circle and then mark off the corresponding arc length on the unit circle as many times as they need to for 0, 1, 2, 3, 4, 5, and 6 radians. They...
Activity
Analyze Math

Analyze Math: Sectors and Circles Problems

For Students 9th - 10th Standards
Try these three problems regarding area of sectors, length of arcs, and central angles. The problems will challenge and intrigue sharp geometry students. Detailed written solutions are included.
Unit Plan
OpenStax

Open Stax: Rotation Angle and Angular Velocity

For Students 9th - 10th
In the following interactive students will begin to define arc length, rotation angle, radius of curvature and angular velocity. They will also calculate the angular velocity of a car wheel spin.
Unit Plan
Texas Education Agency

Texas Gateway: Circular Motion & Gravitation: Rotation Angle & Angular Velocity

For Students 11th - 12th
By the end of this section, you will be able to define arc length, rotation angle, radius of curvature, and angular velocity; and to calculate the angular velocity of a car wheel spin.
Activity
Lawrence Hall of Science

The Math Page: Trigonometry: Radian Measure

For Students 9th - 10th Standards
Here is a site that clearly and thoroughly explains the radian measure of angles. There are example problems solved, problems for the student to attempt, and answers to the student problems.
Activity
Math Open Reference

Math Open Reference: Constructions

For Students 9th - 10th Standards
Learn about drawing shapes using only a compass and straight edge or ruler with out measuring any lengths or angles.
Unit Plan
Khan Academy

Khan Academy: Challenge Problems: Inscribed Angles

For Students 9th - 10th Standards
Solve two challenging problems that apply the inscribed angle theorem to find an arc measure or an arc length.
Activity
Texas Instruments

Texas Instruments: Applications of Integrals

For Teachers 9th - 10th
Use the TI-89 to find the area between curves, find arc length, and solve first and second order differential equations. Examples in the activity use calculator screenprints and keystroke instructions to demonstrate the use of the...
Interactive
Mangahigh

Mangahigh: Shape: Circumference of a Circle

For Students 9th - 10th Standards
Determine the circumference of a circle or simple arc lengths.
Unknown Type
Khan Academy

Khan Academy: Inscribed Angles

For Students 9th - 10th Standards
Practice the relationship between inscribed and central angles that are subtended by the same arc length. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.
Unknown Type
Khan Academy

Khan Academy: Inscribed Angles

For Students 9th - 10th Standards
Practice the relationship between inscribed & central angles that are subtended by the same arc length.
Unit Plan
Cuemath

Cuemath: What Is a Radian?

For Students 9th - 10th Standards
A comprehensive guide for learning all about radians with definitions, formulas, the arc length formula, angles, the circumference, the radius, solved examples, and practice questions.
Unit Plan
Khan Academy

Khan Academy: Challenge Problems: Inscribed Shapes

For Students 9th - 10th Standards
Solve three challenging problems that apply properties of inscribed shapes to find an arc length or a missing angle.
Activity
Varsity Tutors

Varsity Tutors: Hotmath: Practice Problems: Applications of Integrals

For Students 9th - 10th
Hotmath provides 24 practice problems dealing with integral applications. Each of the practice problems include a step-by-step guide for solving their application.
Handout
University of St. Andrews (UK)

University of St. Andrews: Elliptic Functions

For Students 9th - 10th
Good site with many of the elliptic functions given.

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