[+] ------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-----------------------------+------------------