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Objectives: BTEOTPSWBAT
• Find points on the Unit Circle.
• Use the Wrapping Function W(t) to find points (x, y) on the Unit Circle.
Find a point on the unit circle at .
The Unit Circle has a radius of 1 unit (r = 1).
3
π
1 3,2 2
÷ ÷
3
π
60°
1
1
2
3
2
Warm-up:
Find a point on the unit circle at .
3
4
π
2 2,
2 2
− ÷ ÷
3
4
π
45°
1
2
2−
2
2
Find a point on the unit circle at .
11
6
π
3 1,
2 2
− ÷ ÷
11
6
π
30°1
3
21
2−
Find a point on the unit circle at . 6
π
3 1,
2 2
÷ ÷
6
π
30°1 1
2
3
2
Find a point on the unit circle at .
2
3
π
1 3,
2 2
− ÷ ÷
2
3
π
60°
1
1
2−
3
2
Find a point on the unit circle at .
7
4
π
2 2,
2 2
− ÷ ÷
7
4
π
45°
12
2−
2
2
Find a point on the unit circle at .
10
3
π−
1 3,
2 2
− ÷ ÷
10
3
π−
60°
1
1
2−
3
2
Objectives: BTEOTPSWBAT
• Find points on the Unit Circle.
• Use the Wrapping Function W(t) to find points (x, y) on the Unit Circle.
t
Now “wrap” the number line around the circle.
Each real number on the number line corresponds to a point (x, y)on the unit circle (r = 1).
Name the point where W(t) is located.
1) ( )W π ( 1,0)= −2) (4 )W π (1,0)=
3) 2
Wπ − ÷
(0, 1)= −
54)
2W
π ÷ (0,1)=
5) ( 3 )W π− ( 1,0)= −
Name the quadrant where W(t) is located.
1) 3
Wπ
÷ I
72)
8W
π ÷
II
23)
3W
π − ÷ III
( )4) 3W II5) ( 3)W − III
26) 3
3W
ππ + ÷ IV
547)
8W
π ÷
II 54*Note: This is different than , which would be in I.
8W
÷
How can you tell if a point is on the Unit Circle?
3 4Is the point , on the Unit Circle?
5 5 ÷
2 223 4
Does 1 ?5 5
+ = ÷ ÷ 9 16
1 25 25
+ =
25 1 25
=
Given , find each of the following:
1) ( )W t−3 4
, 5 5
= − ÷
2) (2 )W tπ +3 4
, 5 5
= ÷
( )3) 4W tπ + 3 4,
5 5 = ÷
3 4: ,
5 5W t → ÷
3 4 3 4Note: : , is the same as W(t)= , .
5 5 5 5W t → ÷ ÷
Given , find each of the following:
5) ( )W tπ −3 4
, 5 5
= − ÷
6) ( )W t π−3 4
, 5 5
= − − ÷
3 4: ,
5 5W t → ÷
( )4) W tπ +3 4
, 5 5
= − − ÷
3 1Prove that the point , is on the Unit Circle?
2 2
÷
2 223 1
12 2
+ = ÷ ÷ 3 1
1 4 4
+ =
4 1 4
=
Find each of the following points on the Unit Circle:
1) :6
Wπ → 3 1
, 2 2
= ÷ ÷
52) :
6W
π →
73)
6W
π ÷
3 1,
2 2
= − ÷ ÷
3 1,
2 2
= − − ÷ ÷
134)
6W
π − ÷ 3 1
, 2 2
= − ÷ ÷
Today’s Assignment:
The Wrapping Function worksheet
& pg. 278 (5 – 12)
Grading Scale:53 – 62 10 points43 – 52 9 points31 – 42 7 points19 – 30 5 points 6 – 18 3 points
