Download College Math Survey Mathematician: 3.3 The Unit Circle Notes

College Math Survey
3.3 The Unit Circle
Mathematician:
Notes 10.20.14
RADIAN vs DEGREE
Convert to Radians
Convert to Radians
30o
Why these values?
Special Right Triangles
300
45o
30o-60o-90o
60o
Convert to Degrees
Convert to Degrees


2
3
45o
o
45o-45o-90o
45
We are now going to connect these ideas to a unit circle.
What would the coordinate of a 30o angle be?
Image
Normally
On a Unit Circle
Coordinate (x, y)
Radian Value
Coordinate (x, y)
Radian Value
Coordinate (x, y)
Radian Value
Y=
x=
What would the coordinate of a 60o angle be?
Image
Normally
On a Unit Circle
Y=
x=
What would the coordinate of a 45o angle be?
Image
Normally
On a Unit Circle
Y=
x=
This is the completed version of the unit circle:
How do you read the unit circle?
sin

6
cos
tan

6

6
=
=
=
Ex 1: Find the exact values.
sin
3

2
cos
3

2
tan
3

2
tan
7

4
Ex 2: Find the exact values.
sin
7

4
cos
Ex 3: NEGATIVES
7

4
Ex 4: TRIG OTHER THAN Sin,Cos,Tan
 5
 3
Find the exact value of tan  

.

 4
 3
Find the exact value of sec 

.

Ex 5: Find the exact value of s in the given interval that has the given circular function value.
A)
Quadrant : II
cos s  
1
2
B)
 3

Quadrant :  , 2 
2

sin s  
3
2
College Math Survey
3.3 The Unit Circle
Mathematician:
Page 113 #1-17 odd, 55, 57
For each value of  , find sin  ,cos  , and tan  .

1)  
sin   _______ cos   ______ tan   _______
2
3)   2
sin   _______ cos   ______ tan   _______
5)   
sin   _______ cos   ______ tan   _______
Find the exact circular function value for each of the following.
7
6
9)
tan
csc
11
6
13)
 7 
cos  

 6 
cos
7
4
17)
 4 
sin  

 3 
7)
sin
11)
15)
3
4
Find the exact value of s in the given interval that has the given circular function value.
55)
 
 ,  ;
2 
sin s 
1
2
57)
 3 
 ,
;
 2 
tan s  3