radian and degree measure lesson 1 - spring grove area ... · radian and degree measure ... ex 2:...
TRANSCRIPT
Radian and Degree Measure
Lesson 1.1
s = r r
r
If Arc length (s) = radius,
then = 1 radian.
For one complete
revolution, = 2
0, 2 6.35 rad
/2 1.57 rad
3.14 rad
3/2 4.72 rad
1 2
3
4 5
6
Quadrant I Quadrant II
Quadrant III Quadrant IV
For positive angles
0, - 2
-6.35 rad
- /2 - 1.57 rad
-
- - 3.14 rad
- 3/2 - 4.72 rad
- 5 - 4
- 3
- 2 - 1
- 6
Quadrant I Quadrant II
Quadrant III Quadrant IV
For negative angles
Ex 1: Estimate the angle to the nearest 1/2 radian.
A.
B.
C.
2.5 rad
3.5 rad
- 1 rad
Ex 2: Determine the quadrant in which each angle lies.
A. /5 B. 7/5
C. - /12 D. - 3.5
Quad I
Quad III
Quad IV 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 B. 5/4
C. - 7/4 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.
A.
/6 + 2
62
6
12
6
13
6
62
6
12
6
11
6
Ex 4 (cont’d): Determine two co-terminal angles (one positive
and one negative) for each angle.
B. 5/6
5
62
Positive:
5
6
12
6
17
6
Negative: 5
62
5
6
12
6
7
6
C. - 2/3
D. /12
2
32
2
3
6
3
4
3
Positive:
Negative: 2
32
2
3
6
3
8
3
122
12
24
1225
12
Positive:
Negative:
12
2
12
24
12
23
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
3 2 xCompl.: x
2 3 3
6
2
6
6
Suppl.:
3 x x
3 3
3 3
2
3
Ex 5 (cont’d): Find, if possible, the complement and
supplement of each angle
B. 3/4
3
4 2
Compl.:
Suppl.: 3
4
x x
3
4 4
4
3
4
4
Complementary angle does not exist.
Homework: p.138 #2-24 even
C. 1 D. 2
Ex 5 (cont’d): Find, if possible, the complement and
supplement of each angle
Compl.:
12
x
x
21
Suppl.: 1 x
x 1
Compl.:
22
Does not
exist.
Suppl.: 2 x
x 2