2.  A unit circle is a circle that has a center
at the origin with a radius of one. The
equation of a unit circle is x 2 + y 2 = 1.
 Using radian measure, we can label the
points on the unit circle that correspond
with the degree measure.

3.  The radian is a unit of plane angle,
equal to 180/ π degrees, or about
57.2958 degrees. It is the standard unit of
angular measurement in all areas of
mathematics beyond the elementary
level.
 http://www.reference.com/browse/Radian

4.  Multiply the degree by π/180 and
simplify but leave it in π form.
 Example
   150  15  5
150     
 180  180 18 6

5.  Multiply the radian by 180/π and simplify
until you are left with only a degree
measure.
 Example
5  180  900 
   300 
3    3

6.  0º = 0
 90º = π/2
 180º = π
 270º = 3π/2
 360º = 2π
Picture made by Sarah Allen

7. Picture made by Sarah Allen

8.  Using the special
right
triangles, we can
start to build the
points on the
circle.
Picture made by Sarah Allen

9.  We now know that a 30º angle has a x
value of square root of three divided by
two and a y value at one half. We can
now convert degrees to radian and
complete that point on the circle.
   30  3 
30     
 180  180 18 6

10. Based on our results,
we found that at π/6
we have the point
square root of three
divided by two and
one half. We can
continue this around
entire unit circle,
which is explained in
the video on the
next slide.
Picture made by Sarah Allen

11. Melodyeducate (2011, Feb 8) Building The Unit Circle. Retrieved October 29, 2012 from
http://www.youtube.com/watch?v=BXLxl6YRvdc

12.  Now that we know how to built the unit
circle we can begin to understand what
it was built for.
  3 1
We know that has the point  , 
6  2 2
 
and can use this to find both sine and cosine.

13.  Cos = adj/hyp and in the unit circle that
is x/1 which is just x
 Sin = opp/hyp and in the unit circle that
is y/1 which is just y
Therefore
cos = x and sin = y and any point on the
unit circle can be seen as ( cos, sin )

14. Therefore…
  3   1
cos    and sin   
6 2 6 2

15.  There is a game for the unit circle that can
be used for helping in the memorization of
the unit circle information. Go to the
following link to use this game to help you
remember the information you just learned.
Click on the unit circle in the lower right
hand corner to follow the link.
*must have an internet connection to visit the game
Felliax08. (2007). Unit circle. Retrieved October 29, 2012 from
http://www.purposegames.com/game/unit-circle-quiz/info
Picture made by Sarah Allen

16. 1. Convert 50º into radian.
2. Convert 5π/7 into degree.
3. What is the sin (π/3)?
4. What is the cos (5π/6)?
5. What is the coordinate point of 5π/4
Write your answers onto a sheet of
paper and turn in to Mrs. Allen by
tomorrow.