1. Angles and the Unit circle
Chapter 13 Section 2
Angles and the Unit circle

2. Parts of an angle
Terminal Side
Vertex
Initial Side

3. Standard Position Vertex is at the center
Initial side is on the + x axis
700

4. Standard Position
If terminal ray is in the II quadrant
300

5. Standard Position
If terminal side is in the III quadrant
200

6. Standard Position
If terminal side is in the IV quadrant
400

7. Find the measure of each angle
110
150
450

8. Negative Angle
If you measure an angle counter clockwise you call can give the angle a negative degree
-400

9. Co-Terminal measures
A negative angle and + angle measure that describe the same angle are called Co- Terminal
-400 and 320o are co-terminal

10. Find the Co Terminal Angle
-350
-2000
-3000
-2820
1850
3300

11. Unit Circle A Circle with a radius of one unit centered on the origin
(1,0)
1 unit

12. Unit Circle
For angles in standard position we use the variable q to show we are talking about an angle ( q
(1,0)
1 unit

13. For any point on the unit circle, we can find the coordinates by using the angle in standard position and the rule
(cos(q) , sin(q))
(cos(300) , sin(300))
300
(1,0)
1 unit

14. Cosine and Sine of 30-60-90 triangles2 1

15. Cosine and Sine of 30-60-90 triangles2 1
300

16. Cosine and Sine of 45-45-90 triangles1
450 1

17. Make a 30-60-90 triangle and look at the coordinates
For angles with a terminal side not in the 1st quadrant
Make a triangle and look at the coordinates
(- , )
1200
(1,0)
1 unit

18. Make a 30-60-90 triangle and look at the coordinates
For angles with a terminal side not in the 1st quadrant use the rule QI (+,+) QII (-,+) QIII (-,-) QIV(+,-)
Make a triangle and look at the coordinates
2100
(1,0)
1 unit
(- ,- )

19. For angles with a terminal side not in the 1st quadrant use the rule QI (+,+) QII (-,+) QIII (-,-) QIV(+,-)
U Try
3000
(1,0)
1 unit
( ,- )

21. Do Now
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