the length of a segment from the center of a circle to its perimeter
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Circle Unit Flashcards
Start studying Circle Unit. Learn vocabulary, terms, and more with flashcards, games, and other study tools.
Circle Unit
Arc
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is a closed segment of a differentiable curve in the two-dimensional plane
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Arc Length
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The distance along the arc
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1/20 Created by Haley_Espinoza
Terms in this set (20)
Arc
is a closed segment of a differentiable curve in the two-dimensional plane
Arc Length
The distance along the arc
Center of Circle
Center of a Circle is a point inside the circle and is at an equal distance from all of the points on its circumference.
Central Angle
The angle in a circle whose vertex is the center of the circle is called the Central Angle.
Chord
a geometric line segment whose endpoints both lie on the circle
Circle
is a simple shape of Euclidean geometry that is the set of all points in a plane that are at a given distance from a given point, the centre.
Circumference
The distance around the edge of a circle (or any curvy shape).
Diameter
A straight line going through the center of a circle connecting two points on the circumference.
Inscribed Angle
Inscribed Angle is defined as the angle formed by two chords that meet at the same point on a circle.
Intercepted Arc
That part of a circle that lies between
two lines that intersect it.
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How to Calculate Arc Length of a Circle, Segment and Sector Area
This guide explains everything you need to know about circles, including calculation of area, segment area, sector area, length of an arc, radians, sine and cosine.
Welcome to Owlcation
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Welcome to Owlcation
How to Calculate Arc Length of a Circle, Segment and Sector Area
Author: Eugene Brennan Updated date: Jan 11, 2022
Eugene is a qualified control/instrumentation engineer Bsc (Eng) and has worked as a developer of electronics & software for SCADA systems.
In this tutorial you'll learn about:
names for different parts of a circle
degrees and radians and how to convert between them
chords, arcs and secants
sine and cosine
how to work out the length of an arc and chord
how to calculate the area of sectors and segments
the equation of a circle in the Cartesian coordinate system
What is a Circle?
"A locus is a curve or other figure formed by all the points satisfying a particular equation."
A circle is a single sided shape, but can also be described as a locus of points where each point is equidistant (the same distance) from the centre.
Circumference, diameter and radius
© Eugene Brennan
Angle Formed by Two Rays Emanating from the Center of a Circle
An angle is formed when two lines or rays that are joined together at their endpoints, diverge or spread apart. Angles range from 0 to 360 degrees.
We often "borrow" letters from the Greek alphabet to use in math and science. So for instance we use the Greek letter "p" which is π (pi) and pronounced "pie" to represent the ratio of the circumference of a circle to the diameter.
We also use the Greek letter θ (theta) and pronounced "the - ta", for representing angles.
An angle is formed by two rays diverging from the centre of a circle. This angle ranges from 0 to 360 degrees
Image © Eugene Brennan
360 degrees in a full circle
Image © Eugene Brennan
Parts of a Circle
A sector is a portion of a circular disk enclosed by two rays and an arc.
A segment is a portion of a circular disk enclosed by an arc and a chord.
A semi-circle is a special case of a segment, formed when the chord equals the length of the diameter.
Arc, sector, segment, rays and chord
Image © Eugene Brennan
What is Pi (π) ?
Pi represented by the Greek letter π is the ratio of the circumference to the diameter of a circle. It's a non-rational number which means that it can't be expressed as a fraction in the form a/b where a and b are integers.
Pi is equal to 3.1416 rounded to 4 decimal places.
What's the Length of the Circumference of a Circle?
If the diameter of a circle is D and the radius is R.
Then the circumference C = πD
But D = 2R Scroll to Continue
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So in terms of the radius R
C = πD = 2πR
What's the Area of a Circle?
The area of a circle is A = πR2
But R = D/2
So the area in terms of the radius R is
A = πR2 = π (D/2)2 = πD2/4
What are Degrees and Radians?
Angles are measured in degrees, but sometimes to make the mathematics simpler and elegant it's better to use radians which is another way of denoting an angle. A radian is the angle subtended by an arc of length equal to the radius of the circle. ( "Subtended" means produced by joining two lines from the end points of the arc to the center).
An arc of length R where R is the radius of a circle, corresponds to an angle of 1 radian
So if the circumference of a circle is 2πR i.e 2π times R, the angle for a full circle will be 2π times 1 radian or 2π radians.
And 360 degrees = 2π radians
A radian is the angle subtended by an arc of length equal to the radius of a circle.
Image © Eugene Brennan
How to Convert From Degrees to Radians
360 degrees = 2π radians
Dividing both sides by 360 gives
1 degree = 2π /360 radians
Then multiply both sides by θ
θ degrees = (2π/360) x θ = θ(π/180) radians
So to convert from degrees to radians, multiply by π/180
How to Convert From Radians to Degrees
2π radians = 360 degrees
Guys, does anyone know the answer?