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Trig Project (6 Trigonomic Functions of Any Angle (sinx=y/r, cosx=x/r,…
Trig Project
6 Trigonomic Functions of Any Angle
sinx=y/r
cosx=x/r
tanx=y/x
cscx=r/y
secx=r/x
cotx=x/y
Fundamental Identities
Pythagorean
sin^2 x + cos^2 x = 1
1 + tan^2 x = sec^2 x
1 + cot^2 x = csc^2 x
Quotient
tan x = sin x/cos x
cot x = cos x/ sin x
Even-Odd
Sin(-x)=-sinx
Csc(-x)=-cscx
Cos(-x)=cosx
Sec(-x)=secx
Tan(-x)=-tanx
Cot(-x)=-cotx
Reciprocal
sin x = 1/csc x
cos x = 1/sec x
tan x = 1/cot x
csc x = 1/sin x
sec x = 1/cos x
cot x = 1/ tan x
Sum and Difference Formulas
Sines
sin (a + b) = sin a cos b - sin b cos a
sin (a - b) = sin a cos b + sin b cos a
Cosines
Cos(a - b) = cos a cos b +sin a sin b
Cos(a + b) = cos a cos b - sin a sin b
Tangent
Tan(a-b)=(tan a - tan b)/(1 + tan a tan b)
Tan(a + b)=(tan a + tan b)/(1 - tan a tan b)
Half Angle Formulas
cos(a/2)= +/- √(1+cosa)/2
sin(a/2)= +/- √(1-cosa)/2
tan(a/2)=
(1-cosa)/(sina)
(sina)/(1+cosa)
+/- √(1-cosa)/(1+cosa)
Double Angle Formulas
cos2x=
2cos(^2)x-1
1-2sin(^2)x
cos(^2)x-sin(^2)x
tan2x=(2tanx)/[1-tan(^2)x]
sin2x=2sinxcosx