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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