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Основные формулы тригонометрии. Таблица частных случаев для тригонометрических функций. Таблица углов sin, cos, tg, ctg - (реферат)

Дата добавления: март 2006г.

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------T---T---T---T---T---T---T---T---T---T---T---T---T---T---T---T---T---¬ ¦ 7a 0 ¦ ¦ _ 7p . 0 ¦ _ 7p . 0 ¦ _ 7p . 0 ¦ _ 7p . 0 ¦ _ 12 7p . 0¦ _ 13 7p . 0¦ _ 15 7p . 0¦ 7p 0 ¦ _ 17 7p . 0¦ _ 15 7p . 0¦ _ 14 7p . 0¦ _ 13 7p . 0¦ _ 15 7p . 0¦ _ 17 7p . 0¦ _ 111 7p . 0¦ 12 7p 0¦ ¦ 7 0 ¦ 10 0 ¦ 16 0 ¦ 14 0 ¦ 13 0 ¦ 12 0 ¦ 13 0 ¦ 14 0 ¦ 16 0 ¦ 1 0 ¦ 16 0 ¦ 14 0 ¦ 13 0 ¦ 12 0 ¦ 13 0 ¦ 14 0 ¦ 16 0 ¦ ¦ +-----+---+---+- _- . -+---+---+-- _- . +- _- . -+---+---+---+-- _- . +-- _- . +---+-- _- . +-- _- . +---+---+ ¦ ¦ ¦ _ 11 . 0 ¦ _ 7? 12 . 0 ¦ _ 7? 13 . 0 ¦ ¦ _ 7? 13 . 0¦ _ 7? 12 . 0 ¦ _ 11 . 0 ¦ ¦ _ 1- 51 1 . 0¦ _ 1- 7? 12 . 0¦ _ 1- 7? 13 . 0¦ ¦ _ 1- 7? 13 . 0¦ _ 1- 7? 12 . 0¦ _ 1-1 . 0 ¦ ¦

¦ 1sin 7a 0¦ 10 0 ¦ 12 0 ¦ 12 0 ¦ 12 0 ¦ 11 0 ¦ 12 0 ¦ 12 0¦ 12 0 ¦ 10 0 ¦ 1 2 0 ¦ 12 0 ¦ 12 0 ¦ 1-1 0 ¦ 12 0¦ 12 0 ¦ 12 0 ¦ 10 0 ¦ +-----+---+- _- . -+- _- . -+---+---+---+-- _- . +-- _- . +---+-- _- . +-- _- . +---+---+---+- _- . -+- _- . -+---+ ¦ ¦ ¦ _ 7? 13 . 0 ¦ _ 7? . 12 0 ¦ _ 11 . 0 ¦ ¦ _ 1-1 . 0¦ _ 1- 7? 12 . 0¦ _ 1- 7? 13 . 0¦ ¦ _ 1- 7? 13 . 0¦ _ 1- 7? 12 . 0¦ _ 1-1 . 0¦ ¦ _ 11 . 0 ¦ _ 7? 12 . 0¦ _ 7? 13 . 0 ¦ ¦

¦ 1cos 7a 0¦ 11 0 ¦ 12 0 ¦ 12 0 ¦ 12 0 ¦ 10 0 ¦ 12 0 ¦ 12 0 ¦ 12 0 ¦ 1-1 0 ¦ 1 2 0 ¦ 12 0 ¦ 12 0 ¦ 10 0 ¦ 12 0 ¦ 12 0 ¦ 12 0 ¦ 11 0 ¦ +-----+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ ¦ ¦ ¦ _ 11 . 0 ¦ ¦ _ 1 . 0 ¦ ¦ _ 1 . 0¦ ¦ _ 1-1 . 0¦ ¦ _ 1 1 . 0¦ ¦ _ 1 . 0 ¦ ¦ _ 1 . 0¦ ¦ _ 1-1 . 0¦ ¦

¦ 1tg 7a 0 ¦ 10 0 ¦ 7? 13 0 ¦ 11 0 ¦ 7? 13 0 ¦ 1- 0 ¦ 1- 7? 13 0¦ 1-1 0 ¦ 7? 13 0¦ 10 0 ¦ 1 7? 13 0¦ 11 0 ¦ 7? 13 0 ¦ 1- 0 ¦ 1- 7? 13 0¦ 1-1 0 ¦ 7? 13 0 ¦ 10 0 ¦

+-----+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ ¦ ¦ ¦ _ 1 . 0 ¦ ¦ _ 1 1 . 0¦ ¦ _ 1-1 . 0¦ ¦ _ 1 . 0¦ ¦ _ 1 . 0¦ ¦ _ 1 1 . 0¦ ¦ _ 1-1 . 0¦ ¦ _ 1 . 0¦ ¦

¦ 1ctg 7a 0¦ 1- 0 ¦ 7? 13 0 ¦ 11 0 ¦ 1 7? 13 0¦ 10 0 ¦ 7? 13 0¦ 1-1 0 ¦ 1- 7? 13 0¦ 1- 0 ¦ 7? 13 0¦ 11 0 ¦ 7? 13 0¦ 10 0 ¦ 7? 13 0 ¦ 1-1 0 ¦ 1- 7? 13 0¦ 1 - 0 ¦

L-----+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+--- 1Таблица частных случаев для тригонометрических у 3р 1авнений. ----- 3\ 0------T-----------T------------T-----------T--------- 3-- 0--T 3¦ 0 3 \ A 0 3¦ 0 30 0 3¦ 0 31 0 3¦ 0 3-1 0 3¦ _ ¦1 . 0 ¦ 3¦ 7 3 \ 0 3¦ 0 3¦ 0 ¦ ¦ 3 2 0 ¦

3¦-------\--- 0¦ 3----------- 0¦ 3------------ 0+ 3----------- 0+ 3------------- 0+ 3¦cos x = a 0 3¦ 0 7p 0 3¦ 0 ¦ ¦ 5 1 0 _ 7p . 0 ¦

3¦ 0 3¦x= 0 32 0 3+ 7p 3*n 0 3¦ 0 3x = 2 7p 3*n 0 ¦ 3x = 7p 3 + 7p 3*n 0¦ 3x= 5 7+ L 33 L 3+2 7p 3*n 0 ¦

¦ 3----------- 0¦ 3----------- 0¦ 3------------ 0+ 3----------- 0+ 3------------- 0+ 3¦ 0 3¦ 0 3¦ 0 _ 7p . 0 3 0 ¦ _ 7p . 0 ¦ 4k 5 0 _ 7p . 0 ¦ 3¦sin x = a 0 3¦ 0 3x = 7p 3*n 0 3¦x = 2 +2 7p 3*n 0¦ 3x= -2 +2 7p 3*n 0¦ 3x=(-1) 0 3*6+2 7p 3n 0¦

3¦ 0 3¦ 0 3¦ 0 ¦ 3 0 ¦ ¦

3+----------- 0¦ 3----------- 0¦ 3------------ 0+ 3----------- 0+ 3------------- 0+ 3¦ ¦ ¦ _ 7p . 3 0¦ 3 _ 7p . 3 0¦ 3 _1 . 0 ¦

3¦tg x = a ¦ x = 2 7p 3*n 0¦ 3x = 4 + 7p 3*n 0¦ 3x= -4 + 7p 3*n 0¦ 3x=arccos 2+ 7p 3n 0¦

3¦ 0¦ 3 0¦ 3 0¦ 3 0¦ ¦

+ 3----------- 0+ 3----------- 0+ 3------------ 0+ 3----------- 0+ 3------------- 0+ ¦ ¦ _ 7p . 0 ¦ _ 7p . 0 ¦ 3 0 _ 33 7p . 0 ¦ _ 31 . 0 ¦ ¦ 3ctg x = a 0 ¦ 3x = 2 0 3+ 7p 3*n¦x = 4 + 7p 3*n 7 0¦ 3x=-4 + 7p 3*n 0 ¦ 3x=arccos2 0 3+ 7p 3n 0¦

¦ ¦ 3 0 3¦ 0 3¦ 0 3¦ 0 ¦

L-----------+------- 3---- 0+ 3------------ 0+ 3----------- 0+ 3- 0------------ 1Основные формулы тригонометрии

4- 5---линия отрыва 4--- 5T--------------- 0T------------¬ 5¦ 0 1sin 52 7a 1 + cos 52 7a 1=1 5¦ 1 7 1 _sin 7a . 5 ¦ 7a 0 - 1альфа 0 ¦

5¦ 0 1tg 7a 1 * ctg 7a 1=1 5¦ 1 tg 7a 1=cos 7a 5 1 5¦ 7b 0 - 1бэта 0 ¦ 5¦ 0 _ 11 . 5¦ 1 5 1 5 _ 1cos 7a . 5 ¦ 7f 1- гамма 0 ¦ 5¦ 0 11+ctg 52 7a 1=sin 52 7a 1 5¦ 1 ctg 7a 1=sin 7a 5 ¦ 7p 0 1- пи 0 ¦ 5¦ 0 _ 11 . 5 ¦ ¦ 1y - 0 1игрек 0 ¦

5¦ 0 11+tg 52 7a 1=cos 52 7a 1 5¦ 0¦ 1x - икс 0 ¦

5+ 1------------------ 5+--------------- 0+- 1----------- 0+ 5¦ 1sin2 7a 1=2sin 7a 1*cos 7a 1 5¦ 1 5формулы сложения 1 0¦ 5¦ 1 5¦ 1cos( 7a 1- 7b 1)=cos 7a 1*cos 7b 1+sin 7a 1*sin 7b 0¦ 5¦ 1cos2 7a 1=cos 52 7a 1-sin 52 7a 1= 5¦ 1cos( 7a 1+ 7b 1)=cos 7a 1*cos 7b 1-sin 7a 1*sin 7b 0¦ 5¦ 1=1-2sin 52 7a 1=2cos 52 7a 1-1 5¦ 1sin( 7a 1- 7b 1)=sin 7a 1*cos 7b 1-cos 7a 1*sin 7b 0¦ 5¦ 1 5¦ 1sin( 7a 1+ 7b 1)=sin 7a 1*cos 7b 1+cos 7a 1*sin 7b 0¦ 5+ 4----------------- 1- 0+------------------------- 1-- 0-+ 5¦ 0 _ 12*tg . 7a 0 5¦ 0 1 0 1 0 _ 1tg 7a 1+tg 7b . 0 ¦ 5¦ 1tg2 7a 1=1-tg 52 7a 1 5¦ 1 tg( 7a 1+ 7b 1)=1-tg 7a 1*tg 7b 0 ¦ 5¦ 1 _ 7a . 1 _sin . 7a 1 _1-cos . 7a 5¦ 0 ¦

5¦ 1tg2 =1+cos 7a 1=sin 7a 1 0¦ 1 0 _ 1tg 7a 1-tg 7b . 0 ¦ 5¦ 1 0¦ 1tg( 7a 1- 7b 1)=1+tg 7a 1*tg 7b 0 ¦

+ 5- 1----------------- 5+ 0----------T-----------------+

¦ _ 7a 1+ 7b . 1 _ 7a 1+ 7b . 5¦ 0 _ 7a . 0 _ 11-cos 7a . 0 ¦ 4¦ 1cos 7a 1+cos 7b 1 = 2cos 2 * cos 2 5¦ 1sin 52 0 12 0 1= 0 12 0 ¦ 4¦ 1 _ 7a 1+ 7b . 1 _ 7a 1- 7b . 5¦ 0 ¦

4¦ 1cos 7a 1-cos 7b 1 = -2sin 2 * sin 2 5¦ 0 _ 7 a . 0 _ 11+cos 7a . 0 ¦ 5¦ 1 _ 7a 1+ 7b . 1 _ 7a 1- 7b . 1 5¦ 1cos 52 0 12 0 1= 0 12 0 ¦ 4¦ 1sin 7a 1+sin 7b 1 = 2sin 0 12 0 1* 0 1cos 0 12 0 5¦ 0 ¦ 4¦ 0 _ 7a 1- 7b . 0 _ 7a 1+ 7b . 5¦ 0 ¦

5¦ 1sin 7a 1-sin 7b 1 = 2sin 0 12 0 1* 0 1cos 0 12 0 5¦ 0 ¦ 4L-- 5------------------------- 4-- 0+-----------------