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 àðãóìåíòîâ
sin(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