1. Radians & The Unit Circle

2. When we discuss radians we are referring to the distance travelled along the track of the rollercoaster y
1 radian: when the distance travelled along the track is the same length as the radius
Unit Circle
center (0, 0)
radius = 1 x 1

3. You go get a corndog. When you come back, the rollercoaster is stuck here… what might have happened??
Watch the rollercoaster & determine the radians

4. Converting Since in a full circle then dividing by 360
or dividing by 2 pi
We can multiple anything by 1 and get an equivalent expression
Used for converting to radians
Used for converting to degrees

5. Convert to radians
1) 2)

6. Convert to Degrees
1) 2)

7. Positive & Negative Co-terminal Angles
Remember when you went and got a corndog? It could have gone around once, twice, etc or even backwards! These are called Co-terminal Angles
Positive- went counterclockwise & answer Positive
Degrees- add 360 (until positive)
Radians- add 2π (until positive)
Negative- went clockwise & answer Negative
Degrees- subtract 360 (until negative)
Radians- subtract 2π (until negative)

8. Degrees
1) Positive Coterminal: Negative Coterminal: 2) Positive Coterminal: =770 Negative Coterminal: = =-310
= 570
= -150
Still Positive!!!!

9. Radians
1) Positive: Negative:

10. You try 240 a) convert to radians b) positive Coterminal in radians
c) negative Coterminal in radians
2) a) convert to degrees
b) positive Coterminal in degrees
c) negative Coterminal in degrees

11. 1) 240 a) b) c) 2) a) 396 b) 756 or 36 c) -324

12. y
We can label the x & y intercepts of the graph because the radius is one
Since the top of the circle is one whole pi, we can count them out by 4ths
This is
(0, 1)
This is
(-1, 0)
(1, 0)
(0, 0) x 1
(0, -1)
This is

13. Since the top of the circle is one whole pi, we can count them out by 6ths
This is
(0, 1)
This is
(-1, 0)
(1, 0)
(0, 0) 1
(0, -1)
This is

14. Lets do all the radians at once… 6ths first- blue & green
(ignore yellow!!!)
(0, 1)
Now the 4ths- yellow & green (ignore blue!!!)
(-1, 0)
(1, 0)
(0, 0) 1
(0, -1)

15. Now you try and fill out the whole circle on your own
(0, 1)
(-1, 0)
(1, 0)
(0, 0)
(0, -1)