### Coterminal Angles and Radian Measure

```Radian Measure and
Coterminal Angles
Take out your
homework from
Friday!!!
Warm-up (1:30 m)

from Friday, describe how you convert
Converting Between Degrees
To convert degrees To convert radians
to radians, multiply to degrees, multiply
by
by
Converting Between and
220
π
5

Picture of Unit Circle with missing degrees
and radian measures. Students fill missing
measures.

 180 
  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
The Unit Circle – An Introduction


1 Revolution = 360°



2 Revolutions = 720°
Positive angles move
counterclockwise around
the circle
Negative angles move
clockwise around the
circle
Sketching
90°
0°
180°
360°
270°

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
7
π
3
7
 5π
3
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
```