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-----------------------------+------------------