Appendix C
773
Fundamental Identities sin 2 θ +cos 2 θ = 1
sin(− θ ) = −sin θ cos(− θ ) = cos θ tan(− θ ) = −tan θ
1+tan 2 θ = sec 2 θ 1+cot 2 θ = csc 2 θ
⎛ ⎝ π ⎛ ⎝ π ⎛ ⎝ π
θ ⎞ θ ⎞ θ ⎞
sin( θ +2 π ) = sin θ cos( θ +2 π ) = cos θ
sin
⎠ = cos θ ⎠ = sin θ ⎠ = cot θ
2 − 2 −
cos
tan( θ + π ) = tan θ
tan
2 −
Law of Sines sin A a = sin B b = sin C c
Law of Cosines a 2 = b 2 + c 2 −2 bc cos A b 2 = a 2 + c 2 −2 ac cos B c 2 = a 2 + b 2 −2 ab cos C Addition and Subtraction Formulas sin( x + y ) = sin x cos y +cos x sin y sin( x − y ) = sin x cos y −cos x sin y cos( x + y ) = cos x cos y −sin x sin y cos( x − y ) = cos x cos y +sin x sin y tan( x + y ) = tan x +tan y 1−tan x tan y tan( x − y ) = tan x −tan y 1+tan x tan y Double-Angle Formulas sin2 x = 2sin x cos x cos2 x = cos 2 x −sin 2 x =2cos 2 x −1=1−2sin 2 x tan2 x = 2tan x 1−tan 2 x
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