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Proof that FG = R₁
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Expression 23: "D" Subscript, 2 , Baseline equals "A" Subscript, 2 , Baseline plus left parenthesis, "A" Subscript, "C" , Baseline minus "R" Subscript, 1 , Baseline , right parenthesis sine StartFraction, "B" Subscript, "O" "C" , Baseline Over 2 , EndFraction
D
2
=
A
2
+
A
C
−
R
1
s
i
n
B
O
C
2
equals
=
5.0 4 2 1 2 0 2 8 9 3 2
5
.
0
4
2
1
2
0
2
8
9
3
2
23
Expression 24: "E" Subscript, 1 , Baseline equals "B" Subscript, 1 , Baseline minus left parenthesis, "B" Subscript, "C" , Baseline minus "R" Subscript, 1 , Baseline , right parenthesis sine StartFraction, "B" Subscript, "O" "C" , Baseline Over 2 , EndFraction
E
1
=
B
1
−
B
C
−
R
1
s
i
n
B
O
C
2
equals
=
- 1.4 2 7 1 9 5 1 1 7 7
-
1
.
4
2
7
1
9
5
1
1
7
7
24
Expression 25: "E" Subscript, 2 , Baseline equals "B" Subscript, 2 , Baseline plus left parenthesis, "B" Subscript, "C" , Baseline minus "R" Subscript, 1 , Baseline , right parenthesis cosine StartFraction, "B" Subscript, "O" "C" , Baseline Over 2 , EndFraction
E
2
=
B
2
+
B
C
−
R
1
c
o
s
B
O
C
2
equals
=
6.2 0 3 5 2 9 2 0 2 8 4
6
.
2
0
3
5
2
9
2
0
2
8
4
25
Expression 26: tangent to the negative 1st power StartFraction, "F" Subscript, 1 , Baseline minus "H" Subscript, 1 , Baseline Over "C" Subscript, 2 , Baseline , EndFraction equals StartFraction, "B" Subscript, "O" "C" , Baseline Over 2 times 2 , EndFraction
t
a
n
−
1
F
1
−
H
1
C
2
=
B
O
C
2
·
2
26
Expression 27: "F" Subscript, 1 , Baseline equals "C" Subscript, 2 , Baseline tangent left parenthesis, StartFraction, "B" Subscript, "O" "C" , Baseline Over 2 times 2 , EndFraction , right parenthesis plus "H" Subscript, 1 , Baseline
F
1
=
C
2
t
a
n
B
O
C
2
·
2
+
H
1
equals
=
0.2 0 3 2 7 5 5 4 9 3 8 7
0
.
2
0
3
2
7
5
5
4
9
3
8
7
27
Expression 28: "F" Subscript, 2 , Baseline equals "O" Subscript, 2 , Baseline
F
2
=
O
2
equals
=
0
0
28
Expression 29: "G" Subscript, 1 , Baseline equals "M" Subscript, 1 , Baseline
G
1
=
M
1
equals
=
negative 3.1 3 3 0 1 9 9 2 8 8 2
−
3
.
1
3
3
0
1
9
9
2
8
8
2
29
Expression 30: "G" Subscript, 2 , Baseline equals "O" Subscript, 2 , Baseline
G
2
=
O
2
equals
=
0
0
30
Expression 31: "H" Subscript, 1 , Baseline equals "C" Subscript, 1 , Baseline
H
1
=
C
1
equals
=
negative 4.2 9 4 4 2 8 8 4 2 3 4
−
4
.
2
9
4
4
2
8
8
4
2
3
4
31
Expression 32: "H" Subscript, 2 , Baseline equals "O" Subscript, 2 , Baseline
H
2
=
O
2
equals
=
0
0
32
Expression 33: "M" Subscript, 1 , Baseline equals "A" Subscript, 1 , Baseline plus "A" Subscript, "M" , Baseline cosine StartFraction, "B" Subscript, "O" "C" , Baseline Over 4 , EndFraction
M
1
=
A
1
+
A
M
c
o
s
B
O
C
4
equals
=
negative 3.1 3 3 0 1 9 9 2 8 8 2
−
3
.
1
3
3
0
1
9
9
2
8
8
2
33
Expression 34: "M" Subscript, 2 , Baseline equals "A" Subscript, "M" , Baseline sine StartFraction, "B" Subscript, "O" "C" , Baseline Over 4 , EndFraction
M
2
=
A
M
s
i
n
B
O
C
4
equals
=
3.3 3 6 2 9 5 4 7 8 2 1
3
.
3
3
6
2
9
5
4
7
8
2
1
34
Graphs
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35
Expression 36: "y" less than 25
y
<
2
5
36
Expression 37: left parenthesis, "M" Subscript, 1 , Baseline plus "R" Subscript, 1 , Baseline cos "t" , "M" Subscript, 2 , Baseline plus "R" Subscript, 1 , Baseline sin "t" , right parenthesis
M
1
+
R
1
c
o
s
t
,
M
2
+
R
1
s
i
n
t
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
domain t Maximum: 360
3
6
0
37
Expression 38: left parenthesis, "M" Subscript, 1 , Baseline plus "R" Subscript, 1 , Baseline cos "t" , "M" Subscript, 2 , Baseline plus "R" Subscript, 1 , Baseline sin "t" , right parenthesis
M
1
+
R
1
c
o
s
t
,
M
2
+
R
1
s
i
n
t
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
domain t Maximum: 360
3
6
0
38
Expression 39: polygon left parenthesis, "A" , "B" , "C" , "D" , right parenthesis
p
o
l
y
g
o
n
A
,
B
,
C
,
D
39
Expression 40: left parenthesis, "R" cos "t" , "R" sin "t" , right parenthesis
R
c
o
s
t
,
R
s
i
n
t
0
0
domain t Minimum:
less than or equal to "t" less than or equal to
≤
t
≤
domain t Maximum: 180
1
8
0
40
Hidden Label: "G" , "M"
G
,
M
Label
equals
=
left parenthesis, negative 3.1 3 3 , 0 , right parenthesis
−
3
.
1
3
3
,
0
left parenthesis, negative 3.1 3 3 , 3.3 3 6 , right parenthesis
−
3
.
1
3
3
,
3
.
3
3
6
41
Hidden Label: "C" , "H"
C
,
H
Label
equals
=
left parenthesis, negative 4.2 9 4 , 7.9 0 9 , right parenthesis
−
4
.
2
9
4
,
7
.
9
0
9
left parenthesis, negative 4.2 9 4 , 0 , right parenthesis
−
4
.
2
9
4
,
0
42
Hidden Label: "M" , "F"
M
,
F
Label
equals
=
left parenthesis, negative 3.1 3 3 , 3.3 3 6 , right parenthesis
−
3
.
1
3
3
,
3
.
3
3
6
left parenthesis, 0.2 0 3 3 , 0 , right parenthesis
0
.
2
0
3
3
,
0
43
Hidden Label: "C" , "F"
C
,
F
Label
equals
=
left parenthesis, negative 4.2 9 4 , 7.9 0 9 , right parenthesis
−
4
.
2
9
4
,
7
.
9
0
9
left parenthesis, 0.2 0 3 3 , 0 , right parenthesis
0
.
2
0
3
3
,
0
44
Points
Points
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45
62
powered by
powered by
O
A
B
F
G
H
C
D
E
M
Start black, "R" Subscript, 1 , Baseline End black
R
1
Start black, "R" Subscript, 1 , Baseline End black
R
1
5 Right Triangles in a Semicircle
"x"
x
"y"
y
"a" squared
a
2
"a" Superscript, "b" , Baseline
a
b
7
7
8
8
9
9
over
÷
functions
(
(
)
)
less than
<
greater than
>
4
4
5
5
6
6
times
×
| "a" |
|
a
|
,
,
less than or equal to
≤
greater than or equal to
≥
1
1
2
2
3
3
negative
−
A B C
StartRoot, , EndRoot
pi
π
0
0
.
.
equals
=
positive
+
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