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Trigonometric identities list page 1/4

Posted in Math Theory by Lia on 11/03/2012

page 1, 2, 3, 4

 

Trigonometric identities – Pages content: 

pg.1

1.  Basic trigonometric identities 

2. Relations between two different trigonometric functions

pg.2 

3.  Angle-addition and angle-subtraction identities

4 Double-angle and triple-angle identities

pg.3 

5.  Half-angles identities.

6. Trigonometric function expressed though half-angle tangent

pg.4 

7. Identities for addition and subtraction of trigonometric functions 

8. Identities for multiplication of trigonometric functions

 

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For the description of the trigonometric functions used in this post look here.

 

1. Basic trigonometric identities.

 

  sin(- alpha) = -sin{alpha}

  cos(- alpha) = cos{alpha}

  tan(- alpha) = - tan{alpha}

  cot(- alpha) = - cot{alpha}

  sec(- alpha) = sec{alpha}

   csc(- alpha) = - csc{alpha}

  sin^2{alpha} + cos^2{alpha} = 1

   tan{alpha} = {{sin{alpha}}/{cos{alpha}}}

   cot{alpha} = {{cos{alpha}}/{sin{alpha}}}

   tan{alpha} = {1/{cot{alpha}}}

   cot{alpha} = {1/{tan{alpha}}}

   sec{alpha} = {1/{cos{alpha}}}

   cos{alpha} = {1}/{sec{alpha}}

   csc{alpha} =  {1/{sin{alpha}}}

   sin{alpha} = {1}/{csc{alpha}}

 

2. Relations between two different trigonometric functions.

 Note:

Click on the formula to see its demonstration.

 

sin{alpha} cos{alpha} tan{alpha} cot{alpha} sec{alpha} csc{alpha}
sin{alpha}  sin{alpha}  {}{}{}{}{}{}{}{pm}{sqrt{1 - cos^2{alpha}}}{}{}{}{}{}{}{} {{tan{alpha}}/{{pm}sqrt{1 + tan^2{alpha}}}} {1}/{{pm}sqrt{1 + cot^2{alpha}}} {{{pm}sqrt{{sec^2{alpha}} - 1}}/{sec{alpha}}}  {1}/{csc{alpha}}
cos{alpha} {}{}{}{}{}{}{}{pm}sqrt{1 - sin^2{alpha}}{}{}{}{}{}{}{}  cos{alpha} {1}/{{pm}sqrt{1 + tan^2{alpha}}} {cot{alpha}}/{{pm}sqrt{1 + cot^2{alpha}}} {1}/{sec{alpha}} {{pm}{sqrt{{csc^2{alpha}} - 1}}}/{csc{alpha}}
tan{alpha} {sin{alpha}}/{{pm}sqrt{1 - sin^2{alpha}}} {{pm}sqrt{1 -cos^2{alpha}}}/{cos{alpha}}  tan{alpha} {1}/{cot{alpha}} {}{}{}{}{}{}{}{pm}sqrt{sec^2{alpha} - 1}{}{}{}{}{}{}{} {1}/{{pm}sqrt{csc^2{alpha} - 1}}
cot{alpha} {{pm}sqrt{1 - sin^2{alpha}}}/{sin{alpha}} {cos{alpha}}/{{pm}sqrt{1 - cos^2{alpha}}} {1}/{tan{alpha}}  cot{alpha} {1}/{{pm}sqrt{sec^2{alpha} - 1}} {}{}{}{}{}{}{}{pm}sqrt{{csc^2{alpha}} - 1}{}{}{}{}{}{}{}
sec{alpha} {1}/{{pm}sqrt{1 - sin^2{alpha}}} {1}/{cos{alpha}} {}{}{}{}{}{}{}{pm}sqrt{1 + tan^2{alpha}}{}{}{}{}{}{}{} {{pm}sqrt{1 + cot^2{alpha}}}/{cot{alpha}}  sec{alpha} {csc{alpha}}/{{pm}sqrt{csc^2{alpha} - 1}}
csc{alpha} {1}/{sin{alpha}} {1}/{{pm}sqrt{1 - cos^2{alpha}}} {{{pm}sqrt{1 + tan^2{alpha}}}/{tan{alpha}}}  {}{}{}{}{}{}{}{pm}sqrt{1 + cot^2{alpha}}{}{}{}{}{}{}{} {sec{alpha}}/{{pm}sqrt{sec^2{alpha} - 1}}  csc{alpha}

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