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#1 2006-03-30 09:01:07

MathsIsFun
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Trigonometry Formulas

Trigonometry Formulas


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

#2 2006-04-02 15:47:49

ganesh
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Re: Trigonometry Formulas

In a right-angled triangle,

Sinθ= Opposite Side/Hypotenuse

Cosθ= Adjacent 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

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)


Character is who you are when no one is looking.
 

#3 2006-04-04 00:51:54

ganesh
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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


Character is who you are when no one is looking.
 

#4 2006-04-22 01:47:56

ganesh
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Re: Trigonometry Formulas

Formulas which express the sum or difference in product









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












Character is who you are when no one is looking.
 

#5 2006-04-22 01:55:24

ganesh
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Re: Trigonometry Formulas

Trignometric ratios of Multiple Angles











Trignometric ratios of 3θ







Trignometric ratios of sub-multiple angles








Character is who you are when no one is looking.
 

#6 2006-04-22 02:18:53

ganesh
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Re: Trigonometry Formulas

Properties of Inverse Trignometric Functions



























Character is who you are when no one is looking.
 

#7 2006-04-22 23:50:59

ganesh
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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,


Character is who you are when no one is looking.
 

#8 2006-04-24 23:52:51

ganesh
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Re: Trigonometry Formulas

Hyperbolic Functions











Relation between circular and hyperbolic functions







Addition formulas for Hyperbolic functions







Periods of hyperbolic functions







Inverse Hyperbolic functions






Character is who you are when no one is looking.
 

#9 2006-10-10 22:24:11

Devantè
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Re: Trigonometry Formulas

http://www.mathsisfun.com/forum/latex/3/f/4a072ff3a313890c0c37e9e7bf632f1.gif

 

#10 2006-10-11 05:56:58

Devantè
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Re: Trigonometry Formulas

http://www.mathsisfun.com/forum/latex/3/c/4c70d581c72afbf2c70e5a0fc7e4681.gif
http://www.mathsisfun.com/forum/latex/3/c/78ebb3a8a7eb8f2113fcea0ea289e91.gif

Last edited by Devanté (2006-10-11 05:58:28)

 

#11 2007-09-08 02:22:21

kavish2000
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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

 

#12 2007-11-04 01:00:37

ganesh
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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. smile


Character is who you are when no one is looking.
 

#13 2008-02-01 07:42:32

John E. Franklin
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Re: Trigonometry Formulas

New Formula:

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


igloo myrtilles fourmis
 

#14 2008-11-23 00:47:01

Daniel123
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Re: Trigonometry Formulas

 

#15 2009-05-11 03:46:37

Daniel123
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Re: Trigonometry Formulas

Last edited by Daniel123 (2009-05-11 03:47:10)

 

#16 2012-01-24 14:54:57

bobbym
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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

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