radians

Report
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
degrees or radians.
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
circle 1 radius = 1 radian),
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…
 Degrees to radians
radians/
180°
 Radians to degrees
radians
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 radians
3/
4 radians
-2/
3
radians
3. NOW, find the radian measure for all the angles
on your Unit Circle! HINT: start with the axes…
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
Arc Length (and Radians)…
When your angle is
given in radians,
simply multiply the
radius by the radian
measure:
radians  radius
Your Turn…
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
hours. The radius of Earth is about 6400 km,
and the satellite orbits 2600 km above Earths’
surface. How far does the satellite travel in 1
hour?
Assignment…
 13-3 p. 729: mult of 3 (3-42, not 27);
47, 48, 74

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