```13-3 Radian Measure
(p. 726)
Algebra 2
Prentice Hall, 2007
Objectives…
You will:
Content
 Recall geometric terms related to the parts of a
circle and use them to convert degrees to radians
and vice versa.
 Use the circumference formula to determine arc
length.
Language
 Recognize when an angle’s measure is written in
Recall from Geometry…
 A central angle of a circle is
an angle with its vertex at
the center of a circle.
 An intercepted arc is the
portion of the circle with
endpoints on the sides of
the central angle.
Special Angle
Measurements…
 When a central angle intercepts an
arc that has the same length as the
radius of the circle, the measure of
the angle is defined to be 1 radian.
Special Angle
Measurements…
Because the circumference
of a circle is 2r (and in a unit
there are 2 radians in every
circle.
 360 degrees = 2 radians
Think…
 What do you see?
Conversion Factors…
 Remember “unit analysis”… where you
multiply by whatever fraction it takes to get
rid of the old unit and turn it into the new
one?
✕ new unit /old unit --- cancel 1st top with 2nd
bottom
Ex. Convert 32 feet to inches.
Conversion Factors…
180°
multiply by π
multiply by 180°/π
Examples…
1. Find the radian measure for each angle:
45
180
330
2. Find the degree measure for each angle:
/
3/
-2/
3
3. NOW, find the radian measure for all the angles
Arc Length (with Degrees)…
In Geometry, you
found the length of
an intercepted arc
by multiplying the
circumference by
the fraction of the
circle:

 2r
360
simply multiply the
measure:
Ex. 4 Find the lengths of s and b:
Real World Example
Ex. 5 A weather satellite in a circular orbit
around Earth completes one orbit every 2