1. Section 13.6a
The Unit Circle

2. Positive angle of rotation
The Unit Circle (like any circle) contains 360°
It’s called the Unit Circle because the length of
the radius is 1 π
π/2
r = 1
Positive angle of rotation
is counter clock-wise

3. ((opposite)/(hypotenuse)
The Unit Circle
((opposite)/(hypotenuse) 1 y
(1, 0)  x
(adjacent) / (hypotenuse))
Therefore, the coordinates of any point on the
circle are: (cos , sin )

4. Values of the Unit Circle
sin 30o =
r = 1
30o
cos 30o =

5. Values of the Unit Circle
sin 45o =
r = 1
45o
cos 45o =

6. Values of the Unit Circle
sin 60o =
r = 1
60o
cos 60o =

7. Values of the Unit Circle
sin 135o =
cos 135o =

8. - - - - Signs of Trigonometric Functions + + + A S Quadrant + + +
Sin = Opp/Hyp
Cos = Adj/Hyp
Tan = Opp/Adj + + + A S
Quadrant + + + - - -
I - All + -
II - Sin T C
III - Tan
IV - Cos
All Students Take Calculus

9. 1.) using the unit circle convert each measure from degrees to radians
a) 150° b) 225° c) 480°
2.) using the unit circle convert each measure from radians to degrees
a) b) c)

10. 3.) use the unit circle to find the exact value of each
a) sin 120° b) tan 225°
4.) use the unit circle to find sine, cosine and tangent of each
a) b)

12. Homework
Worksheet 13-3B