1. Introduction to the Six Trigonometric Functions & the Unit Circle
1.2
Introduction to the
Six Trigonometric Functions
&
the Unit Circle

2. (0,1) 
(-1,0) 
(1,0) 
(0,-1)

3.  (?,?) (1,0)  = = 2 (0,1) 1 1 1 y x 2 (-1,0)  x 2 x = 2 (0,-1)
45 1 2
(0,1) 
(?,?) 1 y = 1 2 x
(-1,0) 
(1,0) x
x = 2 2 
(0,-1) = 1 2 y
y = 2 2

4.    (1,0)    (0,1) (-2/2, 2/2) (2/2, 2/2) (-1,0) 
(-2/2, -2/2)
(2/2, -2/2) 
(0,-1)

5.   (?,?) (1,0)  = = 3 1 2 (0,1) 1 y 1 2 x (-1,0)  x x = 1 2
60
30 3 1 2
(0,1) 
 (?,?) 1 y = 1 2 x
(-1,0) 
(1,0) x
x = 1 2 
(0,-1) y 3 1 2 =
y = 3 2

6.      (1,0)      (0,1) (-1/2, 3/2) (1/2, 3/2)
(-2/2, 2/2)
(2/2, 2/2)  
(-1,0) 
(1,0)  
(-2/2, -2/2) 
(2/2, -2/2) 
(-1/2, -3/2) 
(1/2, -3/2)
(0,-1)

7.   (?,?) (1,0)  = = 1 2 3 (0,1) x 3 1 2 1 y (-1,0)  x = 3 2 x
60
30 1 2 3
(0,1)  x 3 1 2 =
 (?,?) 1 y
(-1,0) 
(1,0)
x = 3 2 x 
(0,-1) = 1 2 y
y = 1 2

8.        (1,0)        (0,1) (-1/2, 3/2) (1/2, 3/2)
(-2/2, 2/2)
(2/2, 2/2)  
(-3/2, 1/2)
(3/2, 1/2)  
(-1,0) 
(1,0)  
(-3/2, -1/2)
(3/2, -1/2)  
(-2/2, -2/2) 
(2/2, -2/2) 
(-1/2, -3/2) 
(1/2, -3/2)
(0,-1)

9. The six trigonometric functions…
Sine – sin
Cosine – cos
Tangent – tan
Cosecant – csc
Secant – sec
Cotangent - cot

10. Unit Circle Definitions of the
6 Trig. Functions…
csc = 1 y
sin = y
sec = 1 x
cos = x
cot = x y
tan = y x

11. Practice:
Determine the exact value of each without the aid of a calculator.
sin =  3
cos = 5 6
tan = 3 2
csc = 
sec =  2
cot = 4 3

12. Practice:
Determine the exact value of each without the aid of a calculator.
sin 120=
cos 300 =
tan 45=
csc 90=
sec 210=
cot 0=

13. Practice:
Determine the exact value of each without the aid of a calculator.
sin 405=
cos 540 =
tan (-300)=
csc (-120)=
sec 855=
cot 945=

14. Practice:
Determine the exact value of each without the aid of a calculator.
sin =
19 6
cos = 5
Tan =
-2 3
csc =
11 4
sec = 9 2
cot =
-8 3

15. Using the Calculator to Evaluate the
6 Trig. Functions…
sin 212=
sin (212)=
-.5299
cos 319=
cos (319)=
.7547
tan (-402)=
tan (-402)=
-.9004
Be sure your calculator is set in Degree Mode…or you will get an incorrect answer.

16. Using the Calculator to Evaluate the
6 Trig. Functions…
sin /8=
sin (/8)=
.3827
cos 5/7 =
cos (5/7 )=
-.6235
tan (- 2/9 )=
tan (- 2/9 )=
-.8391
Be sure your calculator is set in Radian Mode…or you will get an incorrect answer.

17. What if there is no calculator button?....
csc 48=
sin (48)=
.7431
x-1
=1.3456
Since it is the reciprocal of the sin…use the sin button then reciprocate it… x-1
sec 153=
cos (153)=
-.8910
x-1 =
=-.2679
cot (-75)=
tan (-75)=
x-1