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Special Right Triangles and the Unit Circle
1
February 20, 2009
Feb 1910:24 AM
hypotenuse
opposite
adjacent
5.2 Right Triangle Trigonometry
Objective: Find rectangular points on the unit circle.
Special Right Triangles and the Unit Circle
2
February 20, 2009
Feb 1910:25 AM
hypotenuse
opposite
adjacent
The "BIG 3" functions are defined:
SOH CAH TOA
Special Right Triangles and the Unit Circle
3
February 20, 2009
Feb 1910:25 AM
There are three more functions, but they are just reciprocals of the big 3.
sine cosine tangentcosecant secant cotangent
Special Right Triangles and the Unit Circle
4
February 20, 2009
Feb 1910:28 AM
Special Right Triangle Relationships
1
1245
45
o
o
1
23
30
60
o
o
Special Right Triangles and the Unit Circle
5
February 20, 2009
Feb 193:54 PM
Fill in the degrees and radians for every multiple of 45 and 30.oo
Special Right Triangles and the Unit Circle
6
February 20, 2009
Feb 1910:29 AM
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
Special Right Triangles and the Unit Circle
7
February 20, 2009
Feb 1910:29 AM
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
Special Right Triangles and the Unit Circle
8
February 20, 2009
Feb 1910:29 AM
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
Special Right Triangles and the Unit Circle
9
February 20, 2009
Feb 1910:29 AM
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
Special Right Triangles and the Unit Circle
10
February 20, 2009
Feb 1910:58 AM
(1, 0 )(1, 0 )
(0, 1 )
(0, 1 )
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
Special Right Triangles and the Unit Circle
11
February 20, 2009
Feb 1910:58 AM
(1, 0 )(1, 0 )
(0, 1 )
(0, 1 )
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
( +, + )( , + )
( , )( +, )
Special Right Triangles and the Unit Circle
12
February 20, 2009
Feb 1910:29 AM
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360x
yr
Special Right Triangles and the Unit Circle
13
February 20, 2009
Feb 1910:29 AM
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
opposite
adjacent
hypotenuse
Special Right Triangles and the Unit Circle
14
February 20, 2009
Feb 1910:29 AM
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
opposite
adjacent
hypotenuse
x
yr
Special Right Triangles and the Unit Circle
15
February 20, 2009
Feb 1910:29 AM
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360
opposite
adjacent
hypotenuse
x
yr
sin = yr
cos = xr
tan = yx
Special Right Triangles and the Unit Circle
16
February 20, 2009
Feb 194:10 PM
5.2 A worksheet
#'s: 714, 1535 odds