All about Circles
![Picture](/uploads/3/8/0/4/38046799/9292650.jpg?167)
Arc: any connected part of the circle
![Picture](/uploads/3/8/0/4/38046799/222194.jpg?162)
Intercepted Arc: That part of a circle that lies between two lines that intersect it.
Conditions of an Arc Intercept/Intercepted Arc
A) an angle intercepts an Arc if and only if the endpoints of the arc lie on the angle.
B) all points of the arc, except the endpoints arc in the interior of the circle
C) each side of the angle contains an endpoint of the arc
s = rθ
A) an angle intercepts an Arc if and only if the endpoints of the arc lie on the angle.
B) all points of the arc, except the endpoints arc in the interior of the circle
C) each side of the angle contains an endpoint of the arc
s = rθ
Concepts in finding Degrees, Rad and pi
1deg. = 0.1475 rad or pi/180
181deg. = pi/rad
1 rad = 180/pi or 57.3
Degrees to Rad
Example:
60deg. to Rad
60deg x pi/180rad = pi/3rad
Rad to Degrees
Example
2.3 rad x 180deg./piRad
(2.3) x (180)/pi(3.14159)
181deg. = pi/rad
1 rad = 180/pi or 57.3
Degrees to Rad
Example:
60deg. to Rad
60deg x pi/180rad = pi/3rad
Rad to Degrees
Example
2.3 rad x 180deg./piRad
(2.3) x (180)/pi(3.14159)
Measurement of Arc length in Radian
In general, if the angle of a sector, θ is measured in degree, then the length of its arc
S = θ/360 x 2piR
If θ is measured in radians then the length of its arc, S = θ/2piR x 2piR or S : θ/2piR x 2piR
2piR = 360deg.
s = rθ
Degree Vs. Radian
![Picture](/uploads/3/8/0/4/38046799/154554_orig.jpg)
Degree - (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of plane angle, representing 1⁄360 of a full rotation.
![Picture](/uploads/3/8/0/4/38046799/3372660_orig.gif)
Radian - is the standard unit of angular measure, used in many areas of mathematics. An angle's measurement in radians is numerically equal to the length of a corresponding arc of a unit circle, so one radian is just under 57.3degrees (when the arc length is equal to the radius)
REMEMBER!
S= rθ pi= 3.14159
r= s/θ 1deg.= 0.017453
θ= s/r r= 57.296
r= s/θ 1deg.= 0.017453
θ= s/r r= 57.296