2. Справочный материал Тригонометрические и гиперболические функции

функция

аргумент

0

/6

/4

/3

/2



sin u

0

1/2

1

0

cos u

1

1/2

0

-1

tg u = sin u/ cos u

0

1

­0

ctg u = cos u/ sin u

1

0

sin(-u) = – sin u

cos(-u) = cos u

tg (-u) = – tg u

ctg (-u) = – ctg u

sin(–u) = sin u

sin(+u) = – sin u

cos(-u) = – cos u

cos(+u) = – cos u

sin(/2–u) = cos u

sin(/2+u) = cos u

cos(/2-u) = sin u

sin(3/2–u) = -cos u

cos(/2+u)= –sin u

sin(3/2+u) = -cos u

cos(3/2-u) = –sin u

cos(3/2+u) = sin u

sin² u+ cos² u = 1

1+tg²u = 1/cos²u

1+ctg²u = 1/sin²u

2sin u cos u = sin2u

cos2u = cos²u-sin²u = 1-2sin²u = 2cos²u-1

sin²u = (1– cos2u)/2

cos²u = (1+cos2u)/2

sin  sin  = (cos(–)–cos(+))/2

sin u = 2tg(u/2)/(1+tg²(u/2))

cos  cos  = (cos(–)+cos(+))/2

cos u = (1–tg²(u/2))/(1+tg²(u/2))

sin  cos  = (sin(–)+sin(+))/2

arcsin  + arccos  = 2

sin  + sin  = 2sin cos

sin  – sin  = 2sin cos

cos  + cos  = 2 cos cos

cos  – cos  = –2 sin sin

sin   

e^ – 1  

ln(1+)  

tg   

b^ – 1   ln b

1 – cos   ²/2

arctg   

arcsin   

 /m