Ðåôåðàòû ïî òåìå Ìàòåìàòèêà
Ðåôåðàò Ìàòåìàòèêà (Øïàðãàëêà) ñêà÷àòü áåñïëàòíî
Ñêà÷àòü ðåôåðàò áåñïëàòíî ↓ [16.97 KB]
Òåêñò ðåôåðàòà Ìàòåìàòèêà (Øïàðãàëêà)
sin è cos ñóììû è ðàçíîñòè äâóõ àðãóìåíòîâsin(a±b)=sin a·cosb±sinb·cosa
cos(a±b)=cosa·cosb`+sin a ·sinb
tg a ± tg b
tg (a±b) = 1 ± tg a · tg b
tg (a±b) =
= ctg a · ctg b`+ 1 = 1 ± tg a · tg b
ctg b ± ctg a tg a ± tg b
Òðèãîíîìåòðè÷åñêèå ôóíêöèè äâîéíîãî àðãóìåíòà
sin2x=2sinx cosx
cos 2x = cos2x - sin2x=
= 2cos2x-1=1-2sin2x
tg2x= 2 tgx
1 - tg2x
sin 3x =3sin x - 4 sin3x
cos 3x= 4 cos3 x - 3 cos
ÂÀÆÍÎ: çíàê ïåðåä êîðíåì çàâèñèò îò òîãî, ãäå íàõ-ñÿ óãîë ½ x:
sin ½ x= ± 1-cosx
2
cos ½ x= ± 1+cosx
2
NB! Ñëåäóþùèå ôîðìóëû ñïðàâåäëèâû ïðè çíàìåíàòåëå ¹ 0 è ñóùåñòâîâàíèÿ ôóíêöèé, âõîäÿùèõ â ýòè ôîðìóëû (tg, ctg)
tg ½ x=sinx =1-cosx =± 1-cosx
1+cosx sinx 1+cosx
ñtg½ x=sinx =1+cosx =± 1+cosx
1-cosx sinx 1-cosx
Ôîðìóëû ïîíèæåíèÿ ñòåïåíè:
sin2 x = 1– cos 2x
2
cos2 x = 1+ cos 2x
2
sin3 x = 3 sin x – sin 3x
4
cos3 x = 3 cos x + cos 3x
4
Ïðåîáðàçîâàíèå ïðîèçâåäåíèÿ äâóõ ôóíêöèé â ñóììó:
2 sinx siny = cos(x-y) – cos(x+y)
2 cosx cosy = cos(x-y)+cos(x+y)
2 sinx cosy = sin(x-y) + sin (x+y)
tgx tgy = tgx + tgy
ctgx + ctgy
ctgx ctgy = ctgx + ctgy
tgx + tgy
tgx ctgy = tgx + ctgy
ctgx + tgy
NB! Âûøåïåðå÷èñëåííûå ôîðìóëû ñïðàâåäëèâû ïðè çíàìåíàòåëå ¹ 0 è ñóùåñòâîâàíèÿ ôóíêöèé, âõîäÿùèõ â ýòè ôîðìóëû (tg, ctg)
sinx ± siny= 2sin x±y cos x`+ y
2 2
cosx + cosy =2cos x+y cos x-y
2 2
cosx - cosy = - 2sin x+y sin x-y
2 2
tgx ± tgy= sin(x±y)
cosx cosy
tgx + ñtgy = cos(x-y)
cosx siny
ctgx - tgy = cos(x+y)
sinx cosy
ctgx±ctgy= sin(y±x)
sinx siny
sin x = 1 x= ½ p +2pn, nÎ Z
sin x = 0 x= pn, nÎ Z
sin x = -1 x= - ½ p +2pn, nÎ Z
sin x = a ,
[a
]
≤ 1
x = (-1)karcsin a + pk, kÎ Z
cosx=1 x=2pn, nÎ Z
cosx=0 x= ½ p +pn, nÎ Z
cosx= -1 x=p +2pn, nÎ