Основные формулы тригонометрии

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------T---T---T---T---T---T---T---T---T---T---T---T---T---T---T---T---T---¬
¦  a  ¦   ¦ p ¦ p ¦ p ¦ p ¦2 p¦3 p¦5 p¦ p ¦7 p¦5 p¦4 p¦3 p¦5 p¦7 p¦11p¦2 p¦
¦     ¦ 0 ¦ 6 ¦ 4 ¦ 3 ¦ 2 ¦ 3 ¦ 4 ¦ 6 ¦   ¦ 6 ¦ 4 ¦ 3 ¦ 2 ¦ 3 ¦ 4 ¦ 6 ¦   ¦
+-----+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
¦     ¦   ¦ 1 ¦?2 ¦?3 ¦   ¦ ?3¦?2 ¦ 1 ¦   ¦-1 ¦-?2¦-?3¦   ¦-?3¦-?2¦-1 ¦   ¦
¦sin a¦ 0 ¦ 2 ¦2  ¦2  ¦ 1 ¦ 2 ¦2  ¦ 2 ¦ 0 ¦ 2 ¦ 2 ¦ 2 ¦-1 ¦ 2 ¦ 2 ¦ 2 ¦ 0 ¦
+-----+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
¦     ¦   ¦?3 ¦?2 ¦ 1 ¦   ¦-1 ¦-?2¦-?3¦   ¦-?3¦-?2¦-1 ¦   ¦ 1 ¦?2 ¦?3 ¦   ¦
¦cos a¦ 1 ¦2  ¦2  ¦ 2 ¦ 0 ¦ 2 ¦ 2 ¦ 2 ¦-1 ¦ 2 ¦ 2 ¦ 2 ¦ 0 ¦ 2 ¦ 2 ¦ 2 ¦ 1 ¦
+-----+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
¦     ¦   ¦ 1 ¦   ¦   ¦   ¦   ¦   ¦-1 ¦   ¦ 1 ¦   ¦   ¦   ¦   ¦   ¦-1 ¦   ¦
¦tg a ¦ 0 ¦?3 ¦ 1 ¦?3 ¦ - ¦-?3¦-1 ¦ ?3¦ 0 ¦ ?3¦ 1 ¦?3 ¦ - ¦-?3¦-1 ¦?3 ¦ 0 ¦
+-----+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
¦     ¦   ¦   ¦   ¦ 1 ¦   ¦-1 ¦   ¦   ¦   ¦   ¦   ¦ 1 ¦   ¦-1 ¦   ¦   ¦   ¦
¦ctg a¦ - ¦?3 ¦ 1 ¦ ?3¦ 0 ¦ ?3¦-1 ¦-?3¦ - ¦ ?3¦ 1 ¦ ?3¦ 0 ¦?3 ¦-1 ¦-?3¦ - ¦
L-----+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+----
        Таблица частных случаев для тригонометрических уравнений.
      -----\------T-----------T------------T-----------T-------------T
      ¦     \ A   ¦     0     ¦     1      ¦    -1     ¦      1      ¦
      ¦      \    ¦           ¦            ¦           ¦      2      ¦
      ¦-------\---¦-----------¦------------+-----------+-------------+
      ¦cos x = a  ¦   p       ¦            ¦           ¦     p       ¦
      ¦           ¦x= 2 + p*n ¦ x = 2 p*n  ¦x = p + p*n¦x= + 3 +2p*n ¦
      ¦-----------¦-----------¦------------+-----------+-------------+
      ¦           ¦           ¦    p       ¦    p      ¦     k  p    ¦
      ¦sin x = a  ¦ x = p*n   ¦x = 2 +2 p*n¦x= -2 +2p*n¦x=(-1) *6+2pn¦
      ¦           ¦           ¦            ¦           ¦             ¦
      +-----------¦-----------¦------------+-----------+-------------+
      ¦           ¦           ¦    p       ¦    p      ¦         1   ¦
      ¦tg x = a   ¦ x = 2 p*n ¦x = 4 + p*n ¦x= -4 +p*n ¦x=arccos 2+pn¦
      ¦           ¦           ¦            ¦           ¦             ¦
      +-----------+-----------+------------+-----------+-------------+
      ¦           ¦    p      ¦    p       ¦   3p      ¦        1    ¦
      ¦ctg x = a  ¦x = 2 + p*n¦x = 4 + p*n ¦x=-4 + p*n ¦x=arccos2 +pn¦
      ¦           ¦           ¦            ¦           ¦             ¦
      L-----------+-----------+------------+-----------+--------------
                     Основные формулы тригонометрии
             ----линия отрыва---T---------------T------------¬
             ¦  sin2a + cos2a=1 ¦       sina    ¦a - альфа   ¦
             ¦   tga * ctga=1   ¦   tga=cosa    ¦b - бэта    ¦
             ¦            1     ¦        cosa   ¦f - гамма   ¦
             ¦  1+ctg2a=sin2a   ¦   ctga=sina   ¦p - пи      ¦
             ¦           1      ¦               ¦y - игрек   ¦
             ¦  1+tg2a=cos2a    ¦               ¦x - икс     ¦
             +------------------+---------------+------------+
             ¦sin2a=2sina*cosa  ¦     формулы сложения       ¦
             ¦                  ¦cos(a-b)=cosa*cosb+sina*sinb¦
             ¦cos2a=cos2a-sin2a=¦cos(a+b)=cosa*cosb-sina*sinb¦
             ¦=1-2sin2a=2cos2a-1¦sin(a-b)=sina*cosb-cosa*sinb¦
             ¦                  ¦sin(a+b)=sina*cosb+cosa*sinb¦
             +------------------+----------------------------+
             ¦     2*tga        ¦             tga+tgb        ¦
             ¦tg2a=1-tg2a       ¦    tg(a+b)=1-tga*tgb       ¦
             ¦  a  sina   1-cosa¦                            ¦
             ¦tg2 =1+cosa=sina  ¦             tga-tgb        ¦
             ¦                  ¦    tg(a-b)=1+tga*tgb       ¦
             +------------------+----------T-----------------+
             ¦              a+b      a+b   ¦     a  1-cosa   ¦
             ¦cosa+cosb = 2cos 2  * cos 2  ¦sin2 2 =  2      ¦
             ¦                 a+b      a-b¦                 ¦
             ¦cosa-cosb = -2sin 2  * sin 2 ¦     a  1+cosa   ¦
             ¦                a+b      a-b ¦cos2 2 =   2     ¦
             ¦sina+sinb = 2sin 2  * cos 2  ¦                 ¦
             ¦                a-b       a+b¦                 ¦
             ¦sina-sinb = 2sin 2   * cos 2 ¦                 ¦
             L-----------------------------+------------------


    
Дата добавления: 23.10.2000