trigonometry in brief
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7/18/2019 Trigonometry in brief
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Trigonometry
Hipparcus – 190 BC to 120 BC – born in Nicaea (now Turkey) was a Greek astronomer who is consiere tobe one o! the "rst to use tri#onometry$
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arts o! a i#ht Trian#*e
H y p o t e n u s e
A
B
CNow+ ima#ine that you mo,e!rom an#*e % to an#*e B sti**
!acin# into the trian#*e$
-ma#ine that you+ the happy!ace+ are stanin# at an#*e %
!acin# into the trian#*e$
The hypotenuse is neither oppositenor adjacent$
.ou wou* be !acin# theperpendicular sie
an stanin# ne/t to thebase$
.ou wou* be !acin# theperpendicular sie
an stanin# ne/t to thebase$
erpenicu*ar
Base
%ryabhatta-nian
athematician
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e,iew
H y p o t e n u s e
H y p o t e n u s
e
erpenicu*ar
Base
%
B
or %n#*e %
This is theerpenicu*ar
This is the Base
or %n#*e B
%
This is the Base
This is theerpenicu*ar
erpenicu*ar
Base
B
ytha#orus'amian
athematician
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Tri# atios
e can use the *en#ths o! the sieso! a ri#ht trian#*e to !orm ratios$
There are 3 i4erent ratios thatwe can make$
5sin# %n#*e % to name the sies5se %n#*e B to name thesies
The ratios are sti** the same asbe!ore66
%
B
Hypotenuse
Base
erpenicu*ar
)(
)(
)(
)(
)(
)(
Base B
lar Perpendicu P
Hypotenuse H
Base B
Hypotenuse H
lar Perpendicu P
)(
)(
)(
)(
)(
)(
lar Perpendicu P
Base B
Base B
Hypotenuse H
lar Perpendicu P
Hypotenuse H
amanu&am-nian
athematician
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Tri# atios
• 7ach o! the 3 ratios has a name
• The names a*so re!er to an an#*e
Hypotenuse
Base
erpenicu*ar %
'ine o! %n#*e %8
H
P
Cosine o! %n#*e% 8
H
B
Tan#ent o! %n#*e% 8
B
P
Cosecant o! %n#*e %8
P
H
'ecant o! %n#*e %8
B
H
Cotan#ent o!%n#*e % 8
P
B
7uc*iGreek
athematician
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Tri# atios
Hypotenuse
Base
erpenicu*ar
-! the an#*e chan#es !rom %to B
The way the ratios are mae isthe same
B
'ine o! %n#*e8
H
P
Cosine o! %n#*e
8 H
B
Tan#ent o! %n#*e8
B
P
Cosecant o! %n#*e8
P
H
'ecant o! %n#*e
8 B
H
Cotan#ent o!%n#*e 8
P
B
B
B B
B
B B
reita#German
athematician
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Tri# atios
• 'ine+ Cosine an Tan#entratios are the most common$ Base
erpenicu*ar %
Hypotenuse• 7ach o! these ratios has anabbre,iation
'in %8
Cos %
8
Tan %8
Cosec%8
'ec %
8
Cot %8
'ine o! %n#*e% 8
H
P
Cosine o! %n#*e
% 8 H
B
Tan#ent o! %n#*e% 8
B
P
Cosecant o!%n#*e % 8
P
H
'ecant o! %n#*e
% 8 B
H
Cotan#ent o!%n#*e % 8
P
B
ohn :ee7n#*ish
athematician
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'HCBHTB
Base%
B
erpenicu*ar
HypotenuseHere is a way to rememberhow to make the ; basic Tri#atios
1) -enti!y the erpenicu*ar sie anBase !or the appropriate an#*e
2) emember <'HCBHTB= an it means >?
'ome eop*e Ha,e Cur*y Beauti!u* Hair To
reser,e Beauty5se the uner*ine *etters to makethe wor 'H?CBH?TB
@uete*et*emish
athematician
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3 10
A%
Birst we wi** "n the 'ine+ Cosine an Tan#ent ratios !or %n#*e %$
Ne/t we wi** "n the 'ine+ Cosine+ an Tan#ent ratios !or %n#*e B Base
erpenicu*ar
emember 'H?CBH?TB
4
3
8
6
54
108
5
3
10
6
==
==
==
B
P
H B
H
P Sin A
=
Cos A
=
Tan A
=
Cosec B
=
Sec B
=
Cot B
=3
4
6
8
53
106
5
4
10
8
==
==
==
P
B
B H
P
H
amerench athematician
7/amp*e
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%*berti-ta*ian athematician
Tri#onometric ratios
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