# Реферат: Математика (Шпаргалка)

sinиcosсуммы и разности двух аргументов

sin(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">±<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">b)=sin <span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">a<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Playbill">·cos<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">b<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">±sin<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">b<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Playbill">·cos<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

cos(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">±<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">b)=cos<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">a<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Playbill">·cos<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">b<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">`+sin <span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">a<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Playbill">·sin<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">b

tg <span Times New Roman"; mso-hansi-font-family:«Times New Roman»;position:relative;top:3.0pt;mso-text-raise: -3.0pt;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">a

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language: EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">±  tg <span Times New Roman";mso-hansi-font-family: «Times New Roman»;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language: EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">b

tg (<span Times New Roman";mso-hansi-font-family:«Times New Roman»;position:relative; top:-3.0pt;mso-text-raise:3.0pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">a

<span Times New Roman";mso-hansi-font-family:«Times New Roman»;position:relative; top:-3.0pt;mso-text-raise:3.0pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">±<span Times New Roman";mso-hansi-font-family:«Times New Roman»;position:relative; top:-3.0pt;mso-text-raise:3.0pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">b) =   1 <span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">±tg <span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">a<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Playbill">· tg <span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">b

tg  (<span Times New Roman";mso-hansi-font-family:«Times New Roman»; position:relative;top:6.0pt;mso-text-raise:-6.0pt;mso-ansi-language:EN-US; mso-char-type:symbol;mso-symbol-font-family:Symbol">a

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;position:relative;top:6.0pt;mso-text-raise:-6.0pt;mso-ansi-language: EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">±<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;position:relative;top:6.0pt;mso-text-raise: -6.0pt;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">b) =

=  ctg <span Times New Roman";mso-hansi-font-family:«Times New Roman»;mso-ansi-language: EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Playbill">·ctg <span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">b<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">`+ 1  =  1 <span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">±tg <span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">a<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Playbill">· tg <span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">b

ctg <span Times New Roman";mso-hansi-font-family:«Times New Roman»;position:relative; top:-3.0pt;mso-text-raise:3.0pt;mso-font-kerning:10.0pt;mso-ansi-language:EN-US; mso-char-type:symbol;mso-symbol-font-family:Symbol">b

<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;position:relative;top:-3.0pt; mso-text-raise:3.0pt;mso-font-kerning:10.0pt;mso-ansi-language:EN-US; mso-char-type:symbol;mso-symbol-font-family:Symbol">± ctg  <span Times New Roman";mso-hansi-font-family:«Times New Roman»; position:relative;top:-3.0pt;mso-text-raise:3.0pt;mso-font-kerning:10.0pt; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">a              tg <span Times New Roman";mso-hansi-font-family:«Times New Roman»; position:relative;top:-3.0pt;mso-text-raise:3.0pt;mso-font-kerning:10.0pt; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">a <span Times New Roman"; mso-hansi-font-family:«Times New Roman»;position:relative;top:-3.0pt; mso-text-raise:3.0pt;mso-font-kerning:10.0pt;mso-ansi-language:EN-US; mso-char-type:symbol;mso-symbol-font-family:Symbol">±  tg <span Times New Roman";mso-hansi-font-family:«Times New Roman»; position:relative;top:-3.0pt;mso-text-raise:3.0pt;mso-font-kerning:10.0pt; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">b

Тригонометрические функциидвойногоаргумента

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

<img src="/cache/referats/2961/image001.gif" v:shapes="_x0000_s1027"><img src="/cache/referats/2961/image002.gif" v:shapes="_x0000_s1026">ВАЖНО: знак перед корнем зависит от  того, где  нах-ся  угол  ½ x:

<img src="/cache/referats/2961/image003.gif" v:shapes="_x0000_s1028">sin ½ x=  <span Times New Roman";mso-hansi-font-family: «Times New Roman»;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language: EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">±

1-cosx

<img src="/cache/referats/2961/image004.gif" v:shapes="_x0000_s1030"><img src="/cache/referats/2961/image005.gif" v:shapes="_x0000_s1029">                                        2

<img src="/cache/referats/2961/image006.gif" v:shapes="_x0000_s1031">cos ½ x=  <span Times New Roman";mso-hansi-font-family: «Times New Roman»;position:relative;top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language: EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">±

1+cosx

2

<img src="/cache/referats/2961/image007.gif" v:shapes="_x0000_s1032"><img src="/cache/referats/2961/image008.gif" v:shapes="_x0000_s1033">NB!Следующие формулы справедливыпри знаменателе <span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-char-type:symbol;mso-symbol-font-family:Symbol">¹

0 и существования функций, входящих в эти формулы (tg, ctg)

<img src="/cache/referats/2961/image006.gif" v:shapes="_x0000_s1034">tg ½ x=sinx=1-cosx=<span Times New Roman";mso-hansi-font-family:«Times New Roman»;position:relative; top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">±

1-cosx

1+cosx   sinx          1+cosx

<img src="/cache/referats/2961/image008.gif" v:shapes="_x0000_s1036"><img src="/cache/referats/2961/image009.gif" v:shapes="_x0000_s1037"><img src="/cache/referats/2961/image007.gif" v:shapes="_x0000_s1035">сtg½ x=sinx=1+cosx=<span Times New Roman";mso-hansi-font-family:«Times New Roman»;position:relative; top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">±

1+cosx

1-cosx   sinx           1-cosx

Формулы понижения степени:

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

Преобразование произведения двух функций в сумму:

2 sinxsiny = cos(x-y) – cos(x+y)

2cosx cosy = cos(x-y)+cos(x+y)

2sinx 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!Вышеперечисленные формулысправедливы при знаменателе <span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-char-type:symbol;mso-symbol-font-family:Symbol">¹

0 и существования функций, входящих в эти формулы (tg, ctg)

sinx <span Times New Roman";mso-hansi-font-family:«Times New Roman»; position:relative;top:4.0pt;mso-text-raise:-4.0pt;mso-ansi-language:EN-US; mso-char-type:symbol;mso-symbol-font-family:Symbol">±

siny= 2sin x<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">±ycos x<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">`+y

2               2

cosx + cosy =2cos x+ycos x-y

2            2

cosx — cosy = — 2sin x+ysin x-y

2            2

tgx <span Times New Roman";mso-hansi-font-family:«Times New Roman»;position:relative; top:4.0pt;mso-text-raise:-4.0pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">±

tgy=   sin(x<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">±y)

cosx cosy

tgx + сtgy =   cos(x-y)

cosx siny

ctgx  — tgy =   cos(x+y)

sinx cosy

ctgx<span Times New Roman";mso-hansi-font-family:«Times New Roman»;position:relative; top:4.0pt;mso-text-raise:-4.0pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">±

ctgy=  sin(y<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">±x)

sinx siny

sin x = 1        x=½<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">p

+2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">pn, n<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">ÎZ

sin x= 0                        x= <span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">p

n, n<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">ÎZ

sin x = -1    x=-½<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">p

+2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">pn, n<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">ÎZ

sin x =a ,     <span Courier New"; mso-ascii-font-family:«Times New Roman»;mso-hansi-font-family:«Times New Roman»; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:«Courier New»"><span Courier New"">[

a<span Courier New"; mso-ascii-font-family:«Times New Roman»;mso-hansi-font-family:«Times New Roman»; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:«Courier New»"><span Courier New"">]<span Courier New"; mso-ascii-font-family:«Times New Roman»;mso-hansi-font-family:«Times New Roman»; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:«Courier New»"><span Courier New"">≤1

x = (-1)karcsin a + <span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">p

k, k<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">ÎZ

cosx=1                        x=2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">p

n, n<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">ÎZ

cosx=0             x=½<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">p

+<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">pn, n<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">ÎZ

cosx=-1                x=<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">p

+2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">pn, n<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">ÎZ

cosx=-½   x=<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">±

2/3 <span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">p+2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">pn, n<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">ÎZ

cosx = a ,     <span Courier New"; mso-ascii-font-family:«Times New Roman»;mso-hansi-font-family:«Times New Roman»; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:«Courier New»"><span Courier New"">[

a<span Courier New"; mso-ascii-font-family:«Times New Roman»;mso-hansi-font-family:«Times New Roman»; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:«Courier New»"><span Courier New"">]<span Courier New"; mso-ascii-font-family:«Times New Roman»;mso-hansi-font-family:«Times New Roman»; mso-bidi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:«Courier New»"><span Courier New"">≤1

x=<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">±

arccosa + 2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">pn, n<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">ÎZ

arccos(-x)=<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">p

— arccos x

arcctg(-x)= <span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">p

— ctg x

tgx= 0                              x= n, n<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">Î

Z

ctgx= 0             x=½<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">p

+<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">pn, n<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">ÎZ

tg x= a        x=arctg a +<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">p

n, n<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">ÎZ

ctg x = a  x=arcctga + <span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">p

n, n<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">ÎZ

Знаки тригонометрических функций в    четвертях:

№f(<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

)

sin

cos

tg

ctg

I

+

+

+

+

II

+

<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">-

<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">-

<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">-

III

<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">-

<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">-

+

+

IY

<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">-

+

<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">-

+

<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">a

рад=<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">p<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-char-type:symbol;mso-symbol-font-family:Symbol">×<span Times New Roman";mso-hansi-font-family:«Times New Roman»; mso-char-type:symbol;mso-symbol-font-family:Symbol">a<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol">°/180<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-char-type:symbol;mso-symbol-font-family:Symbol">°;      <span Times New Roman";mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol; mso-symbol-font-family:Symbol">a<span Times New Roman";mso-hansi-font-family:«Times New Roman»;mso-ansi-language: EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">°=<span Times New Roman";mso-hansi-font-family:«Times New Roman»;mso-char-type:symbol; mso-symbol-font-family:Symbol">a<span Times New Roman";mso-hansi-font-family:«Times New Roman»;mso-ansi-language: EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">°<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">×180<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-char-type:symbol;mso-symbol-font-family:Symbol">°/<span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-char-type:symbol;mso-symbol-font-family:Symbol">p

Формулы ïðèâåäåíèÿ

– <span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.1pt;mso-char-type:symbol;mso-symbol-font-family: Symbol">a

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.1pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">p

/2 <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">±<span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">a

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.1pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">p

<span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">±<span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">a

3/2 <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">p

<span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">±<span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">a

2<span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">p

– <span Times New Roman"; mso-hansi-font-family:«Times New Roman»;letter-spacing:-1.1pt;mso-ansi-language: EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

sin

-sin <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.0pt;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

cos <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.0pt;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

<span Times New Roman";mso-hansi-font-family:«Times New Roman»; position:relative;top:2.0pt;mso-text-raise:-2.0pt;letter-spacing:-1.0pt; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">`

+sin <span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-char-type:symbol;mso-symbol-font-family: Symbol">a

— cos <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.0pt;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

— sin <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.0pt;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

cos

cos <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

<span Times New Roman";mso-hansi-font-family:«Times New Roman»; position:relative;top:2.0pt;mso-text-raise:-2.0pt;letter-spacing:-1.1pt; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">`

+sin <span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.1pt;mso-char-type:symbol;mso-symbol-font-family: Symbol">a

— cos <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

<span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">±

sin <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

cos <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

tg

— tg <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

<span Times New Roman";mso-hansi-font-family:«Times New Roman»; position:relative;top:2.0pt;mso-text-raise:-2.0pt;letter-spacing:-1.1pt; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">`

+ ctg <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

<span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">±

tg <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

<span Times New Roman";mso-hansi-font-family:«Times New Roman»; position:relative;top:2.0pt;mso-text-raise:-2.0pt;letter-spacing:-1.1pt; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">`

+ ctg <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

— tg <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

ctg

— ctg <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

<span Times New Roman";mso-hansi-font-family:«Times New Roman»; position:relative;top:2.0pt;mso-text-raise:-2.0pt;letter-spacing:-1.1pt; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">`

+ tg <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

<span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-ansi-language:EN-US;mso-char-type:symbol; mso-symbol-font-family:Symbol">±

ctg <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

<span Times New Roman";mso-hansi-font-family:«Times New Roman»; position:relative;top:2.0pt;mso-text-raise:-2.0pt;letter-spacing:-1.1pt; mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">`

+ tg <span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.1pt;mso-char-type:symbol;mso-symbol-font-family: Symbol">a

-ctg <span Times New Roman";mso-hansi-font-family:«Times New Roman»; letter-spacing:-1.1pt;mso-char-type:symbol;mso-symbol-font-family:Symbol">a

Значения тригонометрических

функций основных углов:

30<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language: EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">°

45<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language: EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">°

60<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language: EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">°

90<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language: EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">°

180<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language: EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">°

270<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language: EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">°

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">p

/ 6

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">p

/4

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">p

/3

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">p

/2

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">p

3<span Times New Roman"; mso-hansi-font-family:«Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language: EN-US;mso-char-type:symbol;mso-symbol-font-family:Symbol">p

/2

sin

½

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">Ö

2 / 2

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">Ö

3 / 2

1

– 1

cos

1

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">Ö

3 / 2

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">Ö

2 / 2

½

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">-

1

tg

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">Ö

3 / 3

1

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">Ö

3

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">-

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">-

ctg

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">Ö

3

1

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">Ö

3 / 3

<span Times New Roman";mso-hansi-font-family: «Times New Roman»;letter-spacing:-1.0pt;mso-ansi-language:EN-US;mso-char-type: symbol;mso-symbol-font-family:Symbol">-

<span Times New Roman",«serif»;mso-fareast-font-family: «Times New Roman»;mso-ansi-language:RU;mso-fareast-language:RU;mso-bidi-language: AR-SA">
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