Шпаргалка: Шпаргалка по математике

arcctg (ctg a) = a ; aÎ [ 0 ; p]

arcsin(sina)=

1)a - 2pk; aÎ[-p/2 +2pk;p/2+2pk]

2) (2k+1)p - a; aÎ[p/2+2pk;3p/2+2pk]

arccos (cosa) =

1) a-2pk ; aÎ[2pk;(2k+1)p]

2) 2pk-a ; aÎ[(2k-1)p; 2pk]

arctg(tga)= a-pk

aÎ(-p/2 +pk;p/2+pk)

arcctg(ctga) = a -pk

aÎ(pk; (k+1)p)

arcsina = -arcsin (-a)= p/2-arccosa =

= arctg a/Ö(1-a²)

arccosa = p-arccos(-a)=p/2-arcsin a=

= arc ctga/Ö(1-a²)

arctga =-arctg(-a) = p/2 -arcctga =

= arcsin a/Ö(1+a²)

arc ctg a = p-arc cctg(-a) =

= arc cos a/Ö(1-a²)

arctg a = arc ctg1/a =

= arcsin a/Ö(1+a²)= arccos1/Ö(1+a²)

arcsin a + arccos = p/2

arcctg a + arctga = p/2

Тригонометрические уравнения

sin x = m ; |m| = 1

x = (-1)ⁿ arcsin m + pk, kÎ Z

sin x =1 sin x = 0

x = p/2 + 2pk x = pk

sin x = -1