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Trigonometry - Identities
Flashcards to help memorize the various Trigonometry Identities
35
Mathematics
Not Applicable
03/31/2009

Additional Mathematics Flashcards

 


 

Cards

Term

Basic Identities

 

 

 

cos2x + sin2x

Definition

 

 

 

 

1

Term

Basic Identities

 

 

 

cos2x

Definition

 

 

 

 

 

1-sin2x

Term

Basic Identities

 

 

 

sin2x

Definition

 

 

 

 

 

 

1-cos2x

Term

Basic Identities

 

 

 

 

1+tan2x

Definition

 

 

 

 


sec2x
Term

Basic Identities

 

 

 

1+cot2x

Definition

 

 

 

 

csc2x

Term

 Cofunction Identities

 

 

 

 

sin(90°-x)

Definition

 

 

 

 

 

cosX

Term

 Cofunction Identities

 

 

 

 

cos(90°-x)
Definition

 

 

 

 

 

sinX

Term

 Cofunction Identities

 

 

 

 

tan(90°-x)
Definition

 

 

 

 

 

cotX

Term

 Cofunction Identities

 

 

 

 

sec(90°-x)
Definition

 

 

 

 

 

cscX

Term

Negative Identities

 

 

 

 

sin(-x)
Definition

 

 

 

 

 

-sinX

Term

Negative Identities

 

 

 

 

cos(-x)
Definition

 

 

 

 

 

-cosX

Term

Negative Identities

 

 

 

 

tan(-x)
Definition

 

 

 

 

 

-tanX

Term

Sum/Difference Idenitities

 

 

 

 

cos(x+y)

Definition

 

 

 

 

cosXcosY - sinXsinY

Term

Sum/Difference Idenitities

 

 

 

 

cos(x-y)

Definition

 

 

 

 

 

 

cosXcosY + sinXsinY

Term

Sum/Difference Idenitities

 

 

 

 

sin(x+y)

Definition

 

 

 

 

 

sinXcosY + cosXsinY

Term

Sum/Difference Idenitities

 

 

 

 

tan(x+y)

Definition

 

 

 

 

 

 

tanX + tanY

1-tanXtanY

Term

Sum/Difference Idenitities

 

 

 

 

tan(x-y)

Definition

 

 

 

 

tanX - tanY

1+tanXtanY

Term

Double Angle Identities

 

 

 

 

sin2x

Definition

 

 

 

 

2sinXcosX

Term

Double Angle Identities

 

 

 

 

cos2x
Definition

 

 = 2cos2x-1

 

 

= 1-2sin2x

 

 

= cos2X -sin2X

 

 

Term

Double Angle Identities

 

 

 

 

tan2x
Definition

 

 

 

 

 

2tanX

1-tan2X

Term

Half Angle Identities

 

 

 

sin(x/2)

Definition

 

 

 

 

+/- √ 1-cos2x

       2

Term

Half Angle Identities

 

 

 

cos(x/2)

Definition

 

 

 

 

+/- √ 1+cos2x

       2
Term

Half Angle Identities

 

 

 

sin2 (x/2)

Definition

 

 

 



1-cosX

 2

Term

Half Angle Identities

 

 

 

 

 cos2(x/2)

Definition

 

 

 

 

 

1+cosX

2

Term

Half Angle Identities

 

 

 

 

tan(x/2)

Definition

 

 

= 1-cosX

   sinX

 

 

= sinx

    1+cosX

 

 

 

Term

Sum/Difference Identities

 

 

 

sin(x-y)

Definition

 

 

 

 

 

sinXcosY - cosXsinY

Term

Product to Sum Identities

 

 

 

sinXcosY

 

Definition

 

 

 

 

 

½[sin(x+y) + sin(x-y)]

Term

Product to Sum Identities

 

 

 

 

 cosXsinY

Definition

 

 

 

 

 

½[sin(x+y) - sin(x-y)]

Term

Product to Sum Identities

 

 

 

 

sinXsinY

Definition

 

 

 

 

½[cos(x-y) - cos(x+y)]

Term

Product to Sum Identities

 

 

 

cosXcosY

Definition

 

 

 

 

 

½[cos(x+y) + cos(x-y)]

Term

Sum to Product Identities

 

 

 

 

sinX + sin Y

Definition

 

 

 

 

2sin x+y cos x-y

                                   2         2

Term

Product to Sum Identities

 

 

 

 

sinX - sinY

Definition

 

 

 

 

2 cosx+y sinx-y

       2         2
Term

Product to Sum Identities

 

 

 

 

cosX + cosY
Definition

 

 

 

 

 

2 cosx+y cosx-y

       2         2

 

Term

Product to Sum Identities

 

 

 

 

cosX - cosY
Definition

 

 

 

 

 

-2 sinx+y sinx-y

       2         2

 

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