Twinkle Twinkle Little Star Circumference Equals 2πr Length of an arc Arc Length s rθ s π rθ 180 1 Revolution Circumference s 2πr A radian is a unit of an angle equal to the angle at the center of a circle whose arc is equal to the length of ID: 378792
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Slide1
What is a RADIAN?!?!Slide2
♪♪Twinkle Twinkle Little Star
Circumference Equals 2πr♪♪
Length of an arc (Arc Length):
s =
rθ
s = (π
rθ
)/180
1 Revolution (Circumference):
s = 2πr
A radian is a unit of an angle equal to the angle at the center of a circle whose arc is equal to the length of the radius.
How many degrees is a radian??Slide3
Arc Length Example
A
circle/pizza/tire/any round object
has a radius of 6 inches. Find the length of the arc intercepted by a central angle of 120∘. Slide4
Area of a Sector
For a circle of radius 𝑟, the area 𝐴 of a sector with central angle 𝜃 is given by
𝐴
=
(1/2)r
2
𝜃
where
𝜃 is measured in radians.
Example
A sprinkler sprays water over a distance of 30
ft
while rotating through an angle of 150∘. What area of lawn receives water? Slide5
Converting Radians
Degrees
To convert from
radians
to
degrees
, multiply the number of
radians
by
180°
/
π radians. Slide6
Examples
Convert radians to degrees.
Convert radians to degrees. Slide7
Converting Degrees
Radians
To convert from
degrees
to
radians
, multiply the number of
degrees
by
π radians
/
180°
. Slide8
Examples
Convert 90° to radians.
Convert 120° to radians.