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## #1 2006-03-29 10:01:07

MathsIsFun
Registered: 2005-01-21
Posts: 7,710

### Trigonometry Formulas

Trigonometry Formulas

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #2 2006-04-01 17:47:49

ganesh
Registered: 2005-06-28
Posts: 39,682

### Re: Trigonometry Formulas

In a right-angled triangle,

Sinθ= Opposite Side/Hypotenuse

Tanθ= Sinθ/Cosθ  = Opposite Side/Adjacent Side

Cosecθ = 1/Sinθ= Hypotenuse/Opposite Side

Secθ = 1/Cosθ = Hypotenuse/Adjacent Side

Cotθ = 1/tanθ = Cosθ/Sinθ = Adjacent Side/Opposite Side

SinθCosecθ = CosθSecθ = TanθCotθ = 1

Sin(90-θ) = Cosθ, Cos(90-θ) = Sinθ

Sin²θ + Cos²θ = 1

Tan²θ + 1 = Sec²θ

Cot²θ + 1 = Cosec²θ

Addition and subtraction formula:-

Sin(A+B) = SinACosB + CosASinB
Sin(A-B) = SinACosb - CosASinB
Cos(A+B) = CosACosB - SinASinB
Cos(A-B) = CosACosB + SinASinB

Tan(A+B) = (TanA+TanB)/(1-TanATanB)

Tan(A-B) = (TanA - TanB)/(1+TanATanB)

Cot (A+B) = (CotACotB-1)/(CotA + CotB)

Cot(A-B) = (CotACotB+1)/(CotB-CotA)

Sin(A+B)+Sin(A-B) = 2SinACosB

Sin(A+B)-Sin(A-B) = 2CosASinB

Cos(A+B)+Cos(A-B) = 2CosACosB

Edited : Cos(A - B) - Cos(A + B) = 2SinASinB

SinC + SinD = 2Sin[(C+D)/2]Cos[(C-D)/2]

SinC - SinD = 2Cos[(C+D)/2]Sin[(C-D)/2]

CosC + CosD = 2Cos[(C+D)/2]Cos[(C-D)/2]

CosC - CosD = 2Sin[(C+D)/2]Sin[(D-C)/2]

Sin2θ = 2SinθCosθ = (2tanθ)/(1+tan²θ)

Cos2θ = Cos²θ - Sin²θ = 2Cos²θ - 1= 1 - 2Sin²θ =
(1-tan²θ)/(1+tan²θ)

Tan2θ = 2tan θ/(1-tan²θ)

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #3 2006-04-03 02:51:54

ganesh
Registered: 2005-06-28
Posts: 39,682

### Re: Trigonometry Formulas

(Angles are given in degrees, 90 degrees, 180 degrees etc.)

I.
Sin(-θ)=-Sinθ
Cos(-θ) = Cosθ
tan(-θ) = -tanθ
cot(-θ) = -cotθ
sec(-θ) = secθ
cosec(-θ)= - cosecθ

II.
sin(90-θ) = cosθ
cos(90-θ) = sinθ
tan(90-θ) = cotθ
cot(90-θ) = tanθ
sec(90-θ) = cosecθ
cosec(90-θ) = secθ

III.
sin(90+θ) = cosθ
cos(90+θ) = -sinθ
tan(90+θ) = -cotθ
cot(90+θ) = -tanθ
sec(90+θ) = -cosecθ
cosec(90+θ) = secθ

IV.
sin(180-θ) = sinθ
cos(180-θ) = -cosθ
tan(180-θ) = -tanθ
cot(180-θ) = cotθ
sec(180-θ) = -secθ
cosec(180-θ) = cosecθ

V.
sin(180+θ) = -sinθ
cos(180+θ) = -cosθ
tan(180+θ) = tanθ
cot(180+θ) = cotθ
sec(180+θ) = -secθ
cosec(180+θ) = -cosecθ

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #4 2006-04-21 03:47:56

ganesh
Registered: 2005-06-28
Posts: 39,682

### Re: Trigonometry Formulas

Formulas which express the sum or difference in product

Formulae which express products as sums or difference of Sines and Cosines

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #5 2006-04-21 03:55:24

ganesh
Registered: 2005-06-28
Posts: 39,682

### Re: Trigonometry Formulas

Trignometric ratios of Multiple Angles

Trignometric ratios of 3θ

Trignometric ratios of sub-multiple angles

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #6 2006-04-21 04:18:53

ganesh
Registered: 2005-06-28
Posts: 39,682

### Re: Trigonometry Formulas

Properties of Inverse Trignometric Functions

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #7 2006-04-22 01:50:59

ganesh
Registered: 2005-06-28
Posts: 39,682

### Re: Trigonometry Formulas

Properties of Triangles

Sine Formula (or  Law of Sines)

In any ΔABC,

Cosine  Formula (or Law of Cosines)

In any ΔABC,

These  formulas are also written as

Projection formulas

In any ΔABC,

Half-Angles and Sides

In any ΔABC,

Area of  a Triangle

Hero's fromula

Incircle and Circumcircle

A circle which touches the three sides of a traingle internally is called the incircle.The center of the circle is called the incentre and the raidus is called the inradius.

If r is the inradius, then

The  circle which passes through the vertices of a triangle is called the circumcircle of a triangle or circumscribing circle. The centre of this circle is the circumcentre and the radius of the circumcircle is the circumradius.

If R is the circumradius, then

If Δ is the area of the triangle,

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #8 2006-04-24 01:52:51

ganesh
Registered: 2005-06-28
Posts: 39,682

### Re: Trigonometry Formulas

Hyperbolic Functions

Relation between circular and hyperbolic functions

Addition formulas for Hyperbolic functions

Periods of hyperbolic functions

Inverse Hyperbolic functions

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #9 2006-10-10 00:24:11

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

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## #10 2006-10-10 07:56:58

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

### Re: Trigonometry Formulas

Last edited by Devanté (2006-10-10 07:58:28)

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## #11 2007-09-07 04:22:21

kavish2000
Member
Registered: 2007-09-07
Posts: 1

### Re: Trigonometry Formulas

ganesh wrote:

Formulas which express the sum or difference in product

Hey ganesh
i just joined this forum. i am an engineer. Am preparing for CAT exam.
am sure u knw abt CAT. (its this november) . So i was looking for some really interesting geometry and number system stuff
like some patterns or some formulaes
etc

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## #12 2007-11-03 02:00:37

ganesh
Registered: 2005-06-28
Posts: 39,682

### Re: Trigonometry Formulas

Hi kavish2000,
I am sorry for the delay in replying,
Yes, I know about CAT, the general questioning pattern etc.
But what exactly do you want to know in Geometry and Number stuff?
Any prearatory CAT book gives the basics. And CAT doesn't require the highest level of Geometry skills or Number theory skills. Beig familiar with UG level mathematics and to some extent PG level would do.

The wikipedia always has much interesting stuff in geometric and number system, provided you know what exactly are the search words you use, and depending on your luck when choosing the relevance percentage.

There are some other interesting forums, sites on the net. If I were you, I would exhaust all search engines, and just hope I am lucky!

Not many engineers pursue the CAT, and most of them who do are likely to be successful. My cousin is one, just about my age, and he's now with an MNC at middle/top management.

My good wishes to you for the CAT, its November already.

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #13 2008-01-31 08:42:32

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

### Re: Trigonometry Formulas

New Formula:

tan(2u)=2/(cot(u)-tan(u))

igloo myrtilles fourmis

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## #14 2008-11-22 01:47:01

Daniel123
Member
Registered: 2007-05-23
Posts: 663

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## #15 2009-05-10 05:46:37

Daniel123
Member
Registered: 2007-05-23
Posts: 663

### Re: Trigonometry Formulas

Last edited by Daniel123 (2009-05-10 05:47:10)

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## #16 2012-01-23 15:54:57

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Trigonometry Formulas

Hi;

At the request of a member I have cleaned this thread to only reflect proven formulas. Some errors as pointed out by John E. Franklin have now been checked and corrected.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #17 2016-04-26 06:31:45

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Trigonometry Formulas

Hi ganesh;

Please edit post #2, this is probably a typo Cos(A-B) - Cos(A-B) = 2SinASinB

Error spotted by Thuhina.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #18 2017-06-30 19:35:29

ganesh
Registered: 2005-06-28
Posts: 39,682

### Re: Trigonometry Formulas

Hi;

The post has been rectified.

Cos(A - B) - Cos(A + B) = 2SinASinB

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #19 2017-07-02 02:36:38

Member
From: Planet Mars
Registered: 2016-11-15
Posts: 821

### Re: Trigonometry Formulas

and CAT doesn't require the highest level of Geometry skills or Number theory skills. Beig familiar with UG level mathematics and to some extent PG level would do.

Hmm, its obvious because Cat opens the door for IIMs (best institute for management) just as IIT-JEE (or Jee advanced) opens the way for iits. There the problems are much tougher.

Practice makes a man perfect.
There is no substitute to hard work
All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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## #20 2018-04-26 20:48:10

aakashrai1997
Member
Registered: 2018-04-26
Posts: 1

### Re: Trigonometry Formulas

ganesh wrote:

(Angles are given in degrees, 90 degrees, 180 degrees etc.)

I.
Sin(-θ)=-Sinθ
Cos(-θ) = Cosθ
tan(-θ) = -tanθ
cot(-θ) = -cotθ
sec(-θ) = secθ
cosec(-θ)= - cosecθ

II.
sin(90-θ) = cosθ
cos(90-θ) = sinθ
tan(90-θ) = cotθ
cot(90-θ) = tanθ
sec(90-θ) = cosecθ
cosec(90-θ) = secθ

III.
sin(90+θ) = cosθ
cos(90+θ) = -sinθ
tan(90+θ) = -cotθ
cot(90+θ) = -tanθ
sec(90+θ) = -cosecθ
cosec(90+θ) = secθ

IV.
sin(180-θ) = sinθ
cos(180-θ) = -cosθ
tan(180-θ) = -tanθ
cot(180-θ) = cotθ
sec(180-θ) = -secθ
cosec(180-θ) = cosecθ

V.
sin(180+θ) = -sinθ
cos(180+θ) = -cosθ
tan(180+θ) = tanθ
cot(180+θ) = cotθ
sec(180+θ) = -secθ
cosec(180+θ) = -cosecθ

cot(180-θ)=-cotθ
since cot(180-θ)=1/tan(180-θ)

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