1. T1.2e To Create Reference Angle Triangles (Butterfly)
&
T1.2e To Create Reference Angle Triangles (Butterfly)
Pick up a handout and READ through it! Don’t write on it, as it is your project!

2. Find the reference angle:
Lesson Opener:
Find the reference angle: I IV
III II

3. Previous assignment: 90° Patterns? 120° 60° 135° 45° 150° 30° 0° 180°II
90°
Patterns?
120°
60°
135°
45°
150°
30° 0°
180°
360°
210°
330°
225°
315°
III
300° IV
240°
270°

4. Recall the positive and negative values for each quadrant:+Y I IV
III II
(– x, + y)
(+ x, + y) –X +X
(– x, – y)
(+ x, – y) –Y

5. Please remember the Real definition!
The Pythagorean Theorem: The square of the hypotenuse is equal to the sum of the squares of the other two sides.
Please remember the Real definition!
5 x 5 = 25 5
3 x 3 = 9 3 4
= 25
4 x 4 = 16

6. To find Right Triangle Values for Standard Angle Reference Angles using the Unit Circle.IV
III II
30° 1
60°
30° 1
30° x
60° 1
Exact Value?
How do we know where to put each measurement?

7. I IV
III II
30°
150° 1 1
60°
60°
30°
30°
180°
30° 1
30° 1 1
210°
330°

8. What about 60 reference angles?I IV
III II
60° 1
30°
60°
180°

9. What about 45 reference angles?I IV
III II
45° 1
y=x
45°
180°
45° x
(Exact value)

10. 90° 180° 0° 360° 270° Quadrangle Angles (0, 1) (1, 0) (– 1, 0) (0, –1)I IV
III II
(0, 1) 1
180° 0° –1 1
(1, 0)
360°
(– 1, 0)
Let’s do a mock up… –1
270°
(0, –1)

11. Butterfly Project:
Start out in pencil, use pens or markers after you get it the way you want.
Put your name, period, and date at the top of this side.
Use the front of this sheet. Orient it as “landscape”
Choose a length to use as your radius “unit”, that is around 1½” to 3” or about 4 cm to 7 cm. Lightly draw the circle and erase it before you turn it in.
Draw a triangle in EACH quadrant for EACH reference angle.

12. At the top corner, put the actual degree for all standard angles
At the top corner, put the actual degree for all standard angles. Ex: 150 gives a 30reference angle in the second quadrant. DO NOT FORGET THE QUADRANGLE ANGLES.
Put the coordinates for each angle next to it. NOT FORGET THE QUADRANGLE ANGLES.
Use correct positive or negative values.
Color each triangle set (fully) a separate color. Ex: for the triangles that represent 30, color all of those blue, etc. (Color lightly, so that I can see the distinct colors.)

13. Active Learning Assignment: Examples are in My Pictures
Butterfly Project
Due: Thursday,
Examples are in My Pictures