The Map of Trigonometric Functions

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R-formula and Trigonometry

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Exponents

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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