Radian Measure and
Coterminal Angles
Take out your
homework from
Friday!!!
Warm-up (1:30 m)

Using your “Degrees and Radians” handout
from Friday, describe how you convert
between degrees and radians.
Converting Between Degrees
and Radians
To convert degrees To convert radians
to radians, multiply to degrees, multiply
by
by
Converting Between and
Radians, cont
Degrees → Radians
220
Radians → Degrees
π
5

Picture of Unit Circle with missing degrees
and radian measures. Students fill missing
measures.
Radian Measure

 180 
radian  
  57.3
 π 



Another way of measuring angles
Convenient because major measurements of a
circle (circumference, area, etc.) are involve pi
Radians result in easier numbers to use
Radian Measure, cont.
The Unit Circle – An Introduction


Circle with radius of 1
1 Revolution = 360°



2 Revolutions = 720°
Positive angles move
counterclockwise around
the circle
Negative angles move
clockwise around the
circle
Sketching
Radians
90°
0°
180°
360°
270°
Sketching Radians

Trick: Convert the fractions into decimals
and use the leading coefficients of pi
π

2
π
3π

2
2π 
5π
Example #1 6
6π
Example #2 4
π
Example #3 4
 9π
Example #4 7
Your Turn: 12π
7
π
3
Your Turn: 10π
7
 5π
3
Your Turn: 15π
13
17π
9
Experiment
Graph

3
and
2
2
do you notice?
on the axes below. What
Coterminal Angles
co – terminal
with, joint,
or together

ending
Coterminal Angles – angles that end
at the same spot
Coterminal Angles, cont.


Each positive angle has a negative
coterminal angle
Each negative angle has a positive
coterminal angle
Solving for Coterminal Angles
If the angle is
If the angle is less
greater than 2 pi, than 0, add 2 pi
subtract 2 pi
to the given
from the given
angle.
angle.


You may need to add or subtract 2 pi more than
once!!!
Trick: Add or subtract the coefficients of pi
rather than the entire radian measure
Examples: Find a coterminal angle
between 0 and 2 pi
 2π
3
29π
6
Your Turn: Find a coterminal angle
between 0 and 2 pi
 14π
13
18π
5
9π
4
 6π
4
Group Exit Ticket


7
π
17
π
Are
and
coterminal? Why or
6
6
why not?
Exit Ticket, cont.
1.
2.
Multiply:
2 * 18
Rationalize:
2
2