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FORMULE TRIGONOMETRICE

Matematica


FORMULE TRIGONOMETRICE

sin(t+2kπ)=sin t ; cos(t+2kπ)=cos t ; tg(x+kπ)=tg x ; ctg(x+kπ)=ctg x ; (kZ);

sin(-x)=-sin x (impara); cos(-x)=cos x (para) ; tg(-x)=-tg x ; ctg(-x)=ctg x ;

x(π/2;π)sin x=-sin(x-π)

cos x=-cos(x-π)

x(π;3π/2)sin x=-sin(2π-x)

cos x=cos(2π-x)

x(3π/2;2π)sin x=-sin(2π-x)

cos x=cos(2π-x)


cos(a-b)=cos a cos b+sin a sin b ; cos(a+b)=cos a cos b-sin a sin b

sin(a-b)=sin a cos b-cos a sin b ; sin(a+b)=sin a cos b+cos a sin b

tg(a+b)=(tg a+tg b)/(1-tg a tg b); tg(a-b)=(tg a-tg b)/(1+tg a tg b)

sin x=cos(π/2-x); cos x=sin(π/2-x) ; sin2x+cos2x=1;

sin 2x=2sin x cos x ; cos 2x=cos2x-sin2x=1-2sin2x=2cos2x-1 ; tg 2x=2tg x/(1-tg2x)

sin 3x=3sin x-4sin3x ; cos 3x=-3cos x+4cos3x

|cos x|=√(1+cos 2x)/2 ; |sin x|=√(1-cos 2x)/2

tg (x/2)=sin x/(1+cos x) ; sin x=2tg(x/2)/(1+tg2 x/2) ; cos x=(1-tg2 x/2)/(1+tg2 x/2)

sin a+sin b=2sin (a+b)/2 cos (a-b)/2 ; sin a-sin b=2cos (a+b)/2 sin(a-b)/2

cos a+cos b=2cos (a+b)/2 cos (a-b)/2 ; cos a- cos b=-2sin (a+b)/2 sin (a-b)/2

tg a


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