TRIGONOMETRÍA
sen² +cos²=1
tg = sen /cos cotg = cos /sen
sec = 1/cos cosec =1/sen
sen(−)=−sen cos(−)=cos tg(−)=−tg
DERIVADAS
sen(/2−)=cos cos(/2−)=sen
(c)'=0 (x)'=1 (u±v)'=u'±v' (cu)'=cu'
tg(/2−)=cotg
(uv)'=u'v+uv' (u/v)'=(u'v−uv')/v²
sen(/2+)=cos cos(/2+)=−sen
(c/v)'=−cv'/v²
tg(/2+)=−cotg
(x )'=nx ¹ ("x)'=1/2"x
sen(−)=sen cos(−)=−cos tg(−)=−tg
(sen x)'=cos x (cos x)'=−sen x
sen(+)=−sen cos(+)=−cos tg(+)=tg
(tg x)'=1/cos²x (cotg x)'=−1/sen²x
sen(a+b)=sena.cosb+senb.cosa
(arcsen x)'=1/"1−x² (arccos x)'=−1/"1−x²
cos(a+b)=cosa.cosb−sena.senb
(arctg x)'=1/(1+x²) (a)'=alna
tg(a+b)=(tga+tgb)/(1−tga.tgb)
(e)'=e (ln x)'=1/x
sen(a−b)=sena.cosb−senb.cosa
Regla de la cadena:
cos(a−b)=cosa.cosb+sena.senb
(f(g(h(x))))'=f'(g(h(x))).g'(h(x)).h'(x)
tg(a−b)=(tga−tgb)/(1+tga.tgb)
LOGARITMOS
sena+senb=2sen((a+b)/2).cos((a−b)/2)
Log(a.b)=log a +log b Log(a/b)=log a −log b
cosa+cosb=2cos((a+b)/2).cos((a−b)/2)
Log(bª)=a.log b
sena−senb=2sen((a−b)/2).cos((a+b)/2)
cosa−cosb=−2sen((a+b)/2).sen((a−b)/2)
sen2a=2sena.cosa cos2a=cos²a−sen²a
tg2a=2tga/(1−tg²a)
sen(a/2)= ±"(1−cosa)/2 cos(a/2)= ±"(1+cosa)/2
DERIVADAS
tg(a/2)= ± "(1−cosa)/(1+cosa)
TRIGONOMETRÍA
1
(c)'=0 (x)'=1 (u±v)'=u'±v' (cu)'=cu'
sen² +cos²=1
(uv)'=u'v+uv' (u/v)'=(u'v−uv')/v²
tg = sen /cos cotg = cos /sen
(c/v)'=−cv'/v²
sec = 1/cos cosec =1/sen
(x )'=nx ¹ ("x)'=1/2"x
sen(−)=−sen cos(−)=cos tg(−)=−tg
(sen x)'=cos x (cos x)'=−sen x
sen(/2−)=cos cos(/2−)=sen
(tg x)'=1/cos²x (cotg x)'=−1/sen²x
tg(/2−)=cotg
(arcsen x)'=1/"1−x² (arccos x)'=−1/"1−x²
sen(/2+)=cos cos(/2+)=−sen
(arctg x)'=1/(1+x²) (a)'=alna
tg(/2+)=−cotg
(e)'=e (ln x)'=1/x
sen(−)=sen cos(−)=−cos tg(−)=−tg
Regla de la cadena:
sen(+)=−sen cos(+)=−cos tg(+)=tg
(f(g(h(x))))'=f'(g(h(x))).g'(h(x)).h'(x)
sen(a+b)=sena.cosb+senb.cosa
LOGARITMOS
cos(a+b)=cosa.cosb−sena.senb
Log(a.b)=log a +log b Log(a/b)=log a −log b
tg(a+b)=(tga+tgb)/(1−tga.tgb)
Log(bª)=a.log b
sen(a−b)=sena.cosb−senb.cosa
cos(a−b)=cosa.cosb+sena.senb
tg(a−b)=(tga−tgb)/(1+tga.tgb)
sena+senb=2sen((a+b)/2).cos((a−b)/2)
cosa+cosb=2cos((a+b)/2).cos((a−b)/2)
sena−senb=2sen((a−b)/2).cos((a+b)/2)
cosa−cosb=−2sen((a+b)/2).sen((a−b)/2)
sen2a=2sena.cosa cos2a=cos²a−sen²a
tg2a=2tga/(1−tg²a)
sen(a/2)= ±"(1−cosa)/2 cos(a/2)= ±"(1+cosa)/2
tg(a/2)= ± "(1−cosa)/(1+cosa)
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