Radian and Degree Measure
Lesson 1.1
r
s=r

r

If Arc length (s) = radius,
then  = 1 radian.
For one complete
revolution,  = 2
/2 1.57 rad
Quadrant II
Quadrant I
2
1
3

 3.14 rad
Quadrant III
0, 2  6.35 rad
6
4
5
3/2  4.72 rad
For positive angles
Quadrant IV
- 3/2  - 4.72 rad
Quadrant II
Quadrant I
-5
-4
-6
-
- - 3.14 rad
-3
Quadrant III
0, - 2
 -6.35 rad
-1
-2
- /2  - 1.57 rad
For negative angles
Quadrant IV
Ex 1: Estimate the angle to the nearest 1/2 radian.
A.
C.
2.5 rad
- 1 rad
B.
3.5 rad
Ex 2: Determine the quadrant in which each angle lies.
A. /5
B. 7/5

Quad I
Quad III
C. - /12
Quad IV
D. - 3.5
Quad II
0
Acute Angles - angles that have a measure
0 <  < /2 radians
Obtuse Angles - angles that have a measure
/2 <  <  radians
Ex 3: Sketch each angle in standard position.
A. 2/3
C. - 7/4
B. 5/4
D. 3
Coterminal - two angles that share the same terminal side.




One positive angle
+
One negative angle
Two positive angles
Ex 4: Determine two co-terminal angles (one positive and one
negative) for each angle.

6
A.
/6
+ 2

6
 2
 2

12
 
6
6
13

6

12
 
6
6
11

6
Ex 4 (cont’d): Determine two co-terminal angles (one positive
and one negative) for each angle.
B. 5/6
5
Positive:
 2
6
5 12


6
6
17

6
5
 2
Negative:
6
5 12


6
6
7

6
C. - 2/3
2
Positive: 
 2
3
2 6


3
3
2
Negative: 
 2
3
2 6
8



3
3
3
D. /12
Positive:
Negative:
4

3


25

12


23

12
24
 2  
12 12
12
24
 2  
12 12
12
Complementary angles - two angles whose sum is /2 radians
Supplementary angles - two angles whose sum is  radians
Ex 5: Find, if possible, the complement and supplement
of each angle
A. /3
Compl.:
Suppl.:

3

3
x

2
x 
3 2
x 


2 3
6
6


x  

3
3 


3 3


6
2

3
Ex 5 (cont’d): Find, if possible, the complement and
supplement of each angle
B. 3/4
3 
Compl.:

4
2
Complementary angle does not exist.
3
3 4 3
Suppl.:
x  x  


4
4
4
4


4
Ex 5 (cont’d): Find, if possible, the complement and
supplement of each angle
C. 1
D. 2
Compl.:
1 x 
Suppl.:

2
x

2
Compl.:
1
1 x  
x   1
Homework: p.138 #2-24 even
2

Does not
2
exist.
Suppl.:
2 x 
x  2