The Map of Trigonometric Functions
Pythagorean Properties
cos2 x +sin2 x=1
1+tan2x=sec2x
cot2x+1=csc2x
sin x
odd
cos x
even
tan x
odd
sin x/cos x or sec x/csc x
Composite Arguement Properties
cos(A-B)=cosAcosB+sinAsinB
cos(a+B)=cosAcosB-sinAsinB
sin(A+B)=sinAcosB-cosAsinB
sin(A+B)=sinAcosB+cosAsinB
tan(A-B)=(tanA-tanB)/(1+tanAtanB)
tan(A+B)=(tanA+tanB)/(1-tanAtanB)
Double Argument Properties
sin 2x=2sin x cos x
cos 2x=cos2x-sin2x or 1-2sin2x or 2 cos2x-1
tan2x= (2 tan x)/(1-tan2x)
sin2x=1/2(1-cos2x)
cos2x=1/2(1+cos2x)
csc x
odd
1/sin x
sec x
even
1/cos x
cot x
odd
1/tan x
cos x/sin x or csc x/sec x
Sum and Product Properties
2cosAcosB=cos(A+B)+cos(A-B)
2sinAsinB=-cos(A+B)+cos(A-B)
2sinAcosB=sin(A+B)+sin(A-B)
2cosAsinB=sin(A+B)-sin(A-B)
cos x+cos y=2cos 1/2(x+y)cos 1/2(x-y)
cos x-cos y=-2sin 1/2(x+y)sin 1/2(x-y)
sin x+sin y=2sin 1/2(x+y)cos 1/2(x-y)
sin x-sin y=2cos 1/2(x+y)sin 1/2(x-y)
Main topic
Subtopic