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Section 6-2
Unit Circle
I. The Six Trig Functions : Triangle Perspective
B
hypotenuse
opposite
C
A
adjacent
Sin A = ___________ Cos A = ____________ Tan A = __________
Csc A = ___________
Sec A = ____________ Cot A = __________
II. The Six Trig Functions: Circle Perspective
r
y
θ
x
Sin θ = ___________ Cos θ = ____________ Tan θ = __________
Csc θ = ___________ Sec θ = ____________ Cot θ = __________
III.
Six Trig Functions: Unit Circle
A. Quadrantal angles in degrees and radians
cos θ
sin θ
tan θ
sec θ
csc θ
0˚ , 0

2
180˚, 
90˚,
270˚,
3
2
* Helpful Hint:
(x , y)
= (cos θ, sin θ)
and tan θ =
sin 
cos 
B. Special Angles/Reference Angles: 30˚, 45˚, 60˚
1.
Special Triangle Approach
a. 30˚ and 60˚
60˚
30˚
cot θ
b. 45˚
45˚
45˚

6

45˚,
4

60˚,
3
cos θ
sin θ
tan θ
sec θ
csc θ
cot θ
30˚ ,
1. Use the fact that this is a UNIT circle for the quadantal angles
2. Use reference angles
a. If you know 30˚, then you know 150˚, 210˚, and 330˚
b. You also know 60˚, 120˚, 240˚, and 300˚ because it is 30˚ flipped
V. Example Problems
Type #1: P = (x, y) is the point on the unit circle that corresponds to t. Find the exact
values for the six trigonometric functions of t.
1
3
1.  , 

2 
2
Type #2: Find the exact value. Do not use a calculator
2. cos 7π
3. csc

2
Type #3: Find the exact values of each expression. Do not use calc
4. sin 45˚cos 45˚
5. 3 csc


+ cot
3
3
Type #4: Find the exact values of the six trig functions of the given angle. Do not use a
calculator.
6. 210˚
7.
2
3
8.
5
4
Type #5: A point on the terminal side of an angle θ is given. Find the exact values of
the six trig functions.
9. (-3, -2)