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Purple Math
Purplemath: Sectors, Areas, and Arcs
Explains formulas for areas of sectors of circles and lengths of arcs. Demonstrates how to use the formulas in each of degrees and radians.
Paul Dawkins
Paul's Online Notes: Calculus Ii: Parametric Equations and Polar Coordinates
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,...
CK-12 Foundation
Ck 12: Trigonometry: Length of an Arc
[Free Registration/Login may be required to access all resource tools.] Definition and measurement of an arc on a circle,
CK-12 Foundation
Ck 12: Geometry: Circles: Segments and Lengths Study Guide
This study guide on circles covers some vocabulary and theorems about segments and lengths. It is available for download with free registration.
Texas Instruments
Texas Instruments: Math Today Coming Clean About Showering Time
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...
Other
Old Dominion University: Calculus Animations W Mathcad
Explanations and animations of limits, slopes, derivatives, arc length, infinite series, conic sections, cycloids, parametric curves, polar curves, quadric surfaces, and more.
Paul Dawkins
Paul's Online Notes: Calculus Ii: Applications of Integrals
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...
Math2
Math2: Circles
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...
Cuemath
Cuemath: Circles
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...
Illustrative Mathematics
Illustrative Mathematics: F Tf.1 What Exactly Is a Radian?
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...
Analyze Math
Analyze Math: Sectors and Circles Problems
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.
OpenStax
Open Stax: Rotation Angle and Angular Velocity
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.
Texas Education Agency
Texas Gateway: Circular Motion & Gravitation: Rotation Angle & Angular Velocity
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.
Lawrence Hall of Science
The Math Page: Trigonometry: Radian Measure
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.
Math Open Reference
Math Open Reference: Constructions
Learn about drawing shapes using only a compass and straight edge or ruler with out measuring any lengths or angles.
Khan Academy
Khan Academy: Challenge Problems: Inscribed Angles
Solve two challenging problems that apply the inscribed angle theorem to find an arc measure or an arc length.
Texas Instruments
Texas Instruments: Applications of Integrals
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...
Mangahigh
Mangahigh: Shape: Circumference of a Circle
Determine the circumference of a circle or simple arc lengths.
Khan Academy
Khan Academy: Inscribed Angles
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.
Khan Academy
Khan Academy: Inscribed Angles
Practice the relationship between inscribed & central angles that are subtended by the same arc length.
Cuemath
Cuemath: What Is a Radian?
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.
Khan Academy
Khan Academy: Challenge Problems: Inscribed Shapes
Solve three challenging problems that apply properties of inscribed shapes to find an arc length or a missing angle.
Varsity Tutors
Varsity Tutors: Hotmath: Practice Problems: Applications of Integrals
Hotmath provides 24 practice problems dealing with integral applications. Each of the practice problems include a step-by-step guide for solving their application.
University of St. Andrews (UK)
University of St. Andrews: Elliptic Functions
Good site with many of the elliptic functions given.
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