The Map of Trigonometric Functions

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Derivatives

luonut Steve Kangas

The Human Brain

luonut Serena Fowler

Kanye West

luonut Redait Kasahwni

Elements, Compounds, Mixtures

luonut Siti Khadijah

The Map of Trigonometric Functions

Main topic

Subtopic

Sum and Product Properties

sin x-sin y=2cos 1/2(x+y)sin 1/2(x-y)

sin x+sin y=2sin 1/2(x+y)cos 1/2(x-y)

cos x-cos y=-2sin 1/2(x+y)sin 1/2(x-y)

cos x+cos y=2cos 1/2(x+y)cos 1/2(x-y)

2cosAsinB=sin(A+B)-sin(A-B)

2sinAcosB=sin(A+B)+sin(A-B)

2sinAsinB=-cos(A+B)+cos(A-B)

2cosAcosB=cos(A+B)+cos(A-B)

cot x

cos x/sin x or csc x/sec x

1/tan x

sec x

1/cos x

csc x

1/sin x

Double Argument Properties

cos2x=1/2(1+cos2x)

sin2x=1/2(1-cos2x)

tan2x= (2 tan x)/(1-tan2x)

cos 2x=cos2x-sin2x or 1-2sin2x or 2 cos2x-1

sin 2x=2sin x cos x

Composite Arguement Properties

tan(A+B)=(tanA+tanB)/(1-tanAtanB)

tan(A-B)=(tanA-tanB)/(1+tanAtanB)

sin(A+B)=sinAcosB+cosAsinB

sin(A+B)=sinAcosB-cosAsinB

cos(a+B)=cosAcosB-sinAsinB

cos(A-B)=cosAcosB+sinAsinB

tan x

sin x/cos x or sec x/csc x

cos x

even

sin x

odd

Pythagorean Properties

cot2x+1=csc2x

1+tan2x=sec2x

cos2 x +sin2 x=1