My brother's son's sister would be my niece. My niece's mother would be my sister-in-law.

1. THE UNIT CIRCLE
by:
SHIRLY M. MASANGKAY,Ed.D.
Occidental Mindoro National High School
Mamburao, Occidental Mindoro

2. REVIEW

3. REFERENCE ANGLE -
an angle whose measure is
less than 900
which is found
between the terminal side and
the x-axis from an angle in
standard position.
300
450
600
900
1200
1350
1500
1800
2100
2250
3300
3000
2400
2700
3150
3600
00

4. THE UNIT CIRCLE

5. (1,0)
(0, -1)
(0, 1)
(-1, 0)
P (x,y)
r
x
y
O-1
-1
1
1
by Pythagorean Theorem:
OP2
= OM2
+PM2
or
12
= x2
+ y2
x2
+ y2
= 1
The equation of the circle with center at (0,0) and
radius 1.
θ
M

6. (1,0)
s
P (x,y)
1
θ

7. (1,0)
s
P (x,y)
θ

8. 2Π450
450
4
∏
4
3∏
2
∏
4
5∏
4
7 ∏
2
3∏
Π
for 45 degrees
angle
900
v

9. 2Π600
600
3
∏
3
2∏
3
4∏
3
5∏
Π
for 60 degrees
angle

10. 2Π300
6
∏
3
2∏
2
∏
3
4∏
3
5∏
2
3∏
Π
for 30 degrees
angle
300
3
∏
3006
5∏
6
7 ∏
6
11∏

11. COORDINATES OF POINTS ON
THE UNIT CIRCLE
300
450
600
900
1200
1350
1500
1800
2100
2250
3300
3000
2400
2700
3150
3600
00








2
1
,
2
3
4
∏








−
2
1
,
2
3








−−
2
1
,
2
3








−
2
1
,
2
3
6
5∏
6
7∏
6
11∏
6
∏








2
2
,
2
2







−
2
2
,
2
2








−−
2
2
,
2
2








−
2
2
,
2
2
4
3∏
4
5∏
4
7∏
3
∏








2
3
,
2
1








−
2
3
,
2
1








−−
2
3
,
2
1
3
2∏
3
4∏








−
2
3
,
2
1
3
5∏
2Π (1,0)
(0,1)
2
∏
(-1,0) Π
2
3∏
(0,-1)

12. Activity No. 1: Label the unit circle
using the 30-45-60-degree scales
and its corresponding radian
measures.

13. Activity No. 2: Label the unit circle
using the 30-45-60-degree scales
and its corresponding radian
measures and coordinates.

14. Activity No. 3
A. Find the equivalent radian measure of the following degree measures.
1. 300
____________________________
2. 22.50
____________________________
3. 1200
____________________________
4. 3900
____________________________
5. 4800
____________________________
6. 4050
____________________________
7. 4200
____________________________
8. 900
____________________________
9. 6300
____________________________
10. 2400
____________________________
B. Find the equivalent degree measure of the following radian measures.
1. ___________ 6. ___________
2. ___________ 7. ___________
3. ___________ 8. ___________
4. ___________ 9. ___________
5. ___________ 10. ___________
3
∏
3
4∏
4
3∏
6
5∏
6
7∏
∏7
2
5∏
2
3∏
4
7 ∏
6
7∏

15. Activity No.4
COORDINATES OF POINTS ON THE UNIT CIRCLE
Direction: Find the other coordinate of the point of intersection P of the unit circle. The
terminal side of an agle is given. Write the corresponding letter/symbol of the correct
answer in the boxes below.
---- x = S y =
T y = N y =
L x = E x =
A y = W y =
R x = I x =
What relation to you is your brother's son's sister's mother?
3
2
4
3
7
2
4
1
6
5
5
3
3
1
11
6
8
5
5
4
4
7
5
10
4
7
7
53
11
85
5
4
3
5
5
10
3
22
3
5
4
15
6
11
8
39