October 24, 2012
Unit Circle Warm-up!
Your right arm is the initial side and your left arm is
the terminal side. Ready? Let’s go!


43

22
4
7
6

6

-270° 3
Lesson 4.3 Special Triangles
45-45-90 and 30-60-90
The ratio of the 45-45-90
triangle is: 1: 1: √2
The ratio of the 30-60-90
triangle is: 1: √3: 2
Make a table
of the 6 trig
functions for
the special
triangles.
Θ = 30° or π/6
Θ = 45° or π/4
Θ = 60° or π/3
CW 4.3: Pg. 308 #17-26
Use the table we just completed to help you.
What do the Unit Circle and Special
Right Triangles have in common?
• In groups of 2-3, follow the GeoSketchpad
Instructions and answer the questions along
the way on a separate sheet of paper.
60
30
45
45
Let’s go around the circle!
3rd and 4th quadrant
Ms. PD! Show them how to use
the reference angle! It makes
the unit circle easier!
Lesson 4.4
Use the reference angle to help you find all
the points around the unit circle.
A reference angle is the acute angle formed by the
terminal side of θ and the x-axis.
75


For example, the reference angle of 225°
is 45°
.
64
6
4




6

5
6


Sketch the angle, then find the
reference angles for the following:
1. 240°
4
2. 3
11

3.
6
How the reference angle works…
• All you need to remember is the first quadrant
and the reference angle.
Putting it all together!!!
• Each point on the
unit circle
corresponds to the
cosine and sine of
the angle.
• The x-coordinate is
the cosine.
• The y-coordinate is
the sine.
• So each point on the
unit circle is
(cos , sin)
Putting it all together in song!