TRIGONOMETRY LAWS AND IDENTITIES

TRIGONOMETRY

LAWS AND IDENTITIES

TANGENT IDENTITIES

sin tan = cos

cos cot = sin

EVEN/ODD IDENTITIES

sin(-) = - sin() cos(-) = cos() tan(-) = -tan() csc(-) = -csc() sec(-) = sec() cot(-) = -cot()

RECIPROCAL IDENTITIES

1 csc = sin

1 sin = csc

1 sec = cos

1 cos = sec

1 cot = tan

1 tan = cot

DOUBLE ANGLE IDENTITIES

sin(2) = 2 sin cos cos(2) = cos2 - sin2

= 2 cos2 - 1 = 1 - 2 sin2

2 tan tan(2) = 1 - tan2

PYTHAGOREAN IDENTITIES

sin2 + cos2 = 1 tan2 + 1 = sec2 cot2 + 1 = csc2

HALF ANGLE IDENTITIES

sin

2

=

?1

-

cos 2

cos

2

=

?1

+

cos 2

tan

2

=

?11

- +

cos cos

PERIODIC IDENTITIES

sin( + 2) = sin cos( + 2) = cos

tan( + ) = tan csc( + 2) = csc sec( + 2) = sec

cot( + ) = cot

LAW OF COSINES 2 = 2 + 2 - 2 cos 2 = 2 + 2 - 2 cos 2 = 2 + 2 - 2 cos

PRODUCT TO SUM IDENTITIES

1 sin sin = 2 [cos( - ) - cos( + )]

1 cos cos = 2 [cos( - ) + cos( + )]

1 sin cos = 2 [sin( + ) + sin( - )]

1 cos sin = 2 [sin( + ) - sin( - )]

SUM TO PRODUCT IDENTITIES

+

-

sin + sin = 2 sin 2 cos 2

+

-

sin - sin = 2 cos 2 sin 2

+

-

cos + cos = 2 cos 2 cos 2

+

-

cos - cos = -2 sin 2 sin 2

LAW OF SINES IDENTITIES

sin sin sin = =

MOLLWEIDE'S FORMULA

+

=

cos 12 ( sin 12

- )

SUM AND DIFFERENCE IDENTITIES

sin( ? ) = sin cos ? cos sin cos( ? ) = cos cos sin sin

tan ? tan tan( ? ) = 1 tan tan

CONFUNCTION IDENTITIES

sin 2 - = cos

cos 2 - = sin

tan 2 - = cot

csc 2 - = sec

sec 2 - = csc

cot 2 - = tan

MATHS REFERENCE SHEET COLLECTION

A reference sheet for the

senior maths program

Mathematical Applications Mathematical Methods Specialist Mathematics

LAW OF TANGENTS

- +

=

tan tan

12 12

( (

- +

) )

- +

=

tan tan

12 12

( (

- +

) )

- +

=

tan tan

12 12

( (

- +

) )



Flexible Maths Delivery

Hawker College, ACT, Australia

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