trigonometry in brief

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$

%r&it 'araswatSubmitted by :-

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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



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



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



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



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



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



'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



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



%*berti-ta*ian athematician

Tri#onometric ratios



Create By >?

Tri#onometry

Tri#onometry

%r&it 'araswat

C*ass > B

'choo* > G'''?;D+C

E2010 'araswat Bros$

trigonometry in brief

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