Special Triangles
DATE:
1/26
CLASS PERIOD:
PreCalc
UNIT:
U.C.-1
.
LESSON OBJECTIVES:
Students will use Special Triangles to derive angles and coordinates in the Unit Circle (First Quadrant).
This lesson corresponds with Common Core State Standards-Functions-Trigonometric Functions F-TF 3.
Use special triangles to determine geometrically the values of sine, cosine, tangent [for specific angles].
MATERIALS
Unit Circle and Special Triangles WS (CPM
Resource 4.1.1A).
EVALUATION
Completion of Quadrant I during class.
REVIEW
Leg lengths in special right triangles (from
Monday). Radian values for 1st Quadrant angles.
HOMEWORK ASSIGNMENTS
Complete worksheet.
ACTIVITIES TO EXTEND UNDERSTANDING
AND/OR RELATED TOPICS
Hand of Sin or other mnemonic. Think about the
other Quadrants. “All Students Take Calculus”
LITERACY STRATEGIES &
ACCOMMODATIONS
Special Needs students only need to do 30-60-90
triangles.
Schedule
Warm-up (10’)
Activity (30’)
Ending (5’)
Activities
If they completed the Radians Worksheet, review problems from yesterday on the
board: How many radians is: 30? 45? 60? 90? If they weren’t able to complete
the worksheet, walk them through the latter half before starting Special Triangles.
Special Triangles Worksheet. Ask if they recall Monday’s WS. Derive 30-60-90
triangle for them. Have them cut out and label the 30-60-90 triangle. Have them
position it all over the circle to discover patterns and symmetry and label
appropriately. Demonstrate on overhead. Provide progress on overhead as
checkpoints. If time, do 45-45-90 triangle too.
If time, discuss patterns of x- and y- coordinates and other symmetries (memory
devices too: ASTC, Hand of Sin).
(insert CPM Resource 4.1.1A here)
Unit Circle Worksheet 1-3 (Special Triangles)
Name _______________________
Determine the unit circle coordinates for the following angles by sketching the angle
onto a unit circle.
𝜋
a.
𝜃=
c.
𝜃=
e.
𝜃=
g.
𝜃=−
i.
𝜃=−
2
3𝜋
2
7𝜋
4
𝜋
4
5𝜋
6
2𝜋
b.
𝜃=
d.
𝜃=
f.
𝜃=
h.
𝜃=
j.
𝜃=
3
5𝜋
3
8𝜋
3
11𝜋
6
11𝜋
3
The “Hand of Sin” was developed by a colleague of mine, who modified it from his
Cooperating Teacher. Intended to resemble the human hand (the picture below leaves
something to be desired), it helps people remember the order of the coordinates in the
unit circle. Starting at the thumb, the student counts “0, 1, 2, 3, 4.” The Hand has each
of those numbers under a square root symbol. The square root of 0 is 0 and the square
root of 1 is 1, of course, and the square root of 4 is 2. The palm shows that each of these
values is divided by 2 (2 divided by 2 is 1). These increasing values represent the sine
values of the major angles in the first quadrant of the unit circle. Going the other way,
the decreasing values are the values of cosine.