Formule Trigonometrice - cls XI, actualizat cls X

formula fundamentala a trigonometriei

cos²x+sin²x=1

cosx (cu sin)

cosx=sin(π/2-x)

sinx (cu cos)

sinx=cos(π/2-x)

cos(a-b)

cos(a-b)=cosa*cosb+sina*sinb

cos(a+b)

cos(a+b)=cosa*cosb-sina*sinb

sin(a+b)

sin(a+b)=sina*cosb+cosa*sinb

sin(a-b)

sin(a-b)=sina*cosb-cosa*sinb

tg(a+b)

tg(a+b)=(tga+tgb)/(1-tga*tgb)

tg(a-b)

tg(a-b)=(tga-tgb)/(1+tga*tgb)

sin2x

sin2x=2*sinx*cosx

cos2x

cos2x = cos²x - sin²x = 1 - 2sin²x = 2cos²x - 1

tg2x=

tg2x=2tgx/(1-tg²x)

tgx*ctgx=

tgx*ctg=1

cos a*cos b=

cos a*cos b= ½ [ cos(a-b) + cos(a+b) ]

sin a*sin b=

sin a*sin b= ½ [ cos(a-b) - cos(a+b)]

sin a*cos b=

sin a*sin b= ½ [ sin(a-b) + sin(a+b) ]

cos x+cos y

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

cos x-cos y=

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

sin x+sin y=

sin x+sin y=2*sin((x+y)/2)*sin((x-y)/2)

sin x-sin y=

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

ctg x (cu tg)

ctg x=tg (π/2-x)

cos x (cu tg)

cos x = ± 1/(√1+tg²x)

cos(arcsin y)

cos(arcsin y) = √(1-y²)

sin (arccos x)

sin (arccos x) = √(1-x²)

tg (arccosx) =

tg (arccosx) = √(1-x²)/x

arccos x + arcsin x =

arccos x + arcsin x = π/2

tg (arcctg x) =

tg (arcctg x) = 1/x

arctg x + arcctg x =

arctg x + arcctg x = π/2

sin x (cu tg)

sin x = tg x / (√1+tg²x)