4 Nota de Aula Transformações Trigonométricas

MATEMÁTICA Transformações \ue003 trigonométricas \ue003 1 \ue003\ue003\ue003 1 \ue003 \ue003 www.cursounipre.com.br \ue003 (21) \ue003 4101 \u2010 1013 Preparatório \ue003 para \ue003 Concursos \ue003 Militares \ue003 ESFCEX \u2010 ESPCEx \u2010 EsSA \u2010 CHQAO \u2010 AFA \u2010 EP CAr \u2010 EEAER \u2010 EFOMM \u2010 CN \u2010 EN \u2010 Outros \ue003 TRANSFORMAÇÕES \ue003\ue003 TRIGONOMÉTRICAS \ue003 \ue003 \ue003 \ue003 Exemplos: \ue003 \ue003 1) \ue003 Determine \ue003 o \ue003 \ue74f\ue741\ue74a\ue00375° . \ue003 \ue74f\ue741\ue74a\ue00375° \ued4c \ue74f\ue741\ue74a \uf23a 45° \ued45 30° \uf23b \ue003 \ue74f\ue741\ue74a\ue00375° \ued4c \ue74f\ue741\ue74a\ue00345°. cos 30° \ued45 \ue74f\ue741\ue74a\ue00330°. cos 45°\ue003 \ue74f\ue741\ue74a\ue00375° \ued4c \u221a 2 2 . \u221a 3 2 \ued45 1 2 . \u221a 2 2 \ue003 \ue74f\ue741\ue74a\ue00375° \ued4c \u221a 6 4 \ued45 \u221a 2 4 \ue003 \ue74f\ue741\ue74a\ue00375° \ued4c \u221a 6 \ued45 \u221a 2 4 \ue003 \ue003 \ue003 2) \ue003 Determine \ue003 cos 105° . \ue003 \ue725\ue74b\ue74f\ue003135° \ued4c \ue73f\ue74b\ue74f\ue00390°. \ue73f\ue74b\ue74f\ue003 45° \ued46 \ue74f\ue741\ue74a\ue00390°. \ue74f\ue741\ue74a\ue00345°\ue003 cos 135° \ued4c \ued46 \u221a 2 2 \ue003 \ue003 3) \ue003 Determine \ue003 a \ue003 tg \ue003 75°. \ue003 \ue750\ue743\ue00375° \ued4c \ue750\ue743\ue00345° \ued45 \ue750\ue743 \ue00330° 1 \ued46 \ue750\ue743\ue00345°. \ue750\ue743\ue00330° \ue003 \ue750\ue743\ue00375° \ued4c 1\ued45 \u221a 3 3 1\ued46 \u221a 3 3 \ued4c 3\ued45 \u221a 3 3 . 3 3\ued46 \u221a 3 \ued4c\ue003 \ued4c 3\ued45 \u221a 3 3\ued46 \u221a 3 \u2192\ue74e \ue73d \ue73f \ue745 \ue74b \ue74a \ue73d \ue748 \ue745 \ue756 \ue73d \ue74e \ue003 \ued4c 3\ued45 \u221a 3 3\ued46 \u221a 3 . \ued6b3 \ued45 \u221a 3 \ued6f \ued6b3 \ued45 \u221a 3 \ued6f \ued4c 9\ued456 \u221a 3 \ued453 9\ued463 \ue003 \ued4c2 \ued46 \u221a 3 \ue003 \ue003 \ue003 \ue003 \ue003 EXERCÍCIOS \ue003 \ue003\ue003 01) Usando \ue003 as \ue003 fór mulas, \ue003 determine: \ue003 a) \ue003 Sen \ue003 105° e) \ue003 Sen \ue003 225° \ue003 b) \ue003 Cos \ue003 135° f) \ue003 Cos \ue003 225° \ue003 c) Cos \ue003 195° g) \ue003 Cos \ue003 300° \ue003 d) \ue003 Sen \ue003 165° h) \ue003 Sen \ue003 345° \ue003 02) É \ue003 dado \ue003 \ue74f\ue741\ue74a\ue003\ue754 \ued4c \ueb37 \ueb39 ,\ue73f \ue74b \ue749 \ue003 0 \ued4f \ue754 \ued4f \uec17 \ueb36 . \ue003 Calcule \ue003 \ue74f\ue741\ue74a\ue003 \uf240\ue754 \ued46 \uec17 \ueb3a \uf241 , cos \uf240 \uec17 \ueb37 \ued45\ue754 \uf241 \ue003 \ue741 \ue003 \ue750 \ue743 \uf240 \ue754 \ued45 \uec17 \ueb38 \uf241 . \ue003 \ue003 03) Se \ue003 \ue750\ue743\ue003\ue754 \ued4c \ueb35 \ueb36 \ue003\ue741\ue003\ue750\ue743 \ue003\ue755 \ued4c \ueb35 \ueb38 , \ue003 determine \ue003 \ue750\ue743\ue003\uf23a\ue754 \ued45 \ue755 \uf23b . \ue003 \ue003 04) Dado \ue003 \ue750\ue743\ue754 \ued4c \ueb35 \ueb36 , \ue003 calcule \ue003 \ue755\ued4c \ue750 \ue743 \uf23a \ue754 \ued45 45° \uf23b \ued45\ue750 \ue743 \uf23a \ue754 \ued46 45°\uf23b . \ue003 \ue003 05) Dado \ue003 \ue74f\ue741\ue74a\ue003\ue754 \ued4c \ueb37 \ueb39 \ue003\ue741 cos \ue755 \ued4c \ueb39 \ueb35\ueb37 , \ue003 calcule \ue003 cos\ue003 \uf23a\ue754 \ued45 \ue755\uf23b \ue003 sabendo \ue003 que \ue003 0\ued4f\ue754 \ued4f \uec17 \ueb36 \ue003\ue741 \ueb37\uec17 \ueb36 \ued4f\ue755\ued4f2 \ue7e8 . \ue003 \ue003 06) Simplifique \ue003 a \ue003 expressão: \ue003 \ue755\ued4c \ue74f\ue741\ue74a\ue003 \uf240 \ue7e8 2 \ued45 \ue754\uf241 . cos \uf23a \ue7e8\ued46\ue754 \uf23b \ue73f\ue74b\ue74f\ue003 \uf240 3\ue7e8 2 \ued45 \ue754\uf241 . cotg \uf23a \ue7e8\ued45\ue754 \uf23b \ue003 \ue003 07) Dados \ue003 \ue74f\ue741\ue74a\ue003\ue754 \ued4c \uec17 \ueb38 ,\ue73f \ue74b \ue749 \ue003 0 \ued4f \ue754 \ued4f \uec17 \ueb36 ,\ue741 \ue003 \ue754 \ued45 \ue755 \ued4c \uec17 \ueb37 , \ue003 determine \ue003 sen \ue003 y. \ue003 \ue003 08) Dado \ue003 \ue735\ue741\ue74a\ue003\ue754 \ued4c \ueb35 \ueb37 ,\ue003 \ue73f \ue74b \ue749 \ue003 0 \ued4f \ue754 \ued4f \uec17 \ueb36 , \ue003\ue003 calcule \ue003 \ue74f\ue741\ue74a \uf240 \uec17 \ueb3a \ued46\ue754 \uf241 . \ue003 \ue003 09) Simplifique \ue003 a \ue003 expressão: \ue003 \ue74f\ue741\ue74a \uf240 \ue7e8 2 \ued46\ue754 \uf241 . \ue74f \ue741 \ue74a \ue003 \uf23a \ue7e8\ued45\ue754 \uf23b cos \uf23a \ue7e8\ued46 \ue754 \uf23b . cos\uf23a2\ue7e8 \ued46 \ue754 \uf23b \ue003 \ue003 10) Simplifique \ue003 a \ue003 expressão: \ue003 \ue74f \ue741 \ue74a \ue003 3 \ue73d .\ue73f \ue74b \ue74f \ue003 \ue73d \ued45 \ue74f \ue741 \ue74a \ue003 \ue73d .\ue003 \ue73f \ue74b \ue74f \ue003 3 \ue73d cos 7\ue73d\ue003. \ue73f\ue74b\ue74f\ue0033\ue73d \ued45 \ue74f\ue741\ue74a\ue0037\ue73d. \ue003\ue74f\ue741\ue74a\ue0033\ue73d \ue003 \ue003 11) Sabendo \ue003 que \ue003 tg \ue003 (a \ue003 + \ue003 b) \ue003 = \ue003 1 \ue003 e \ue003 tg \ue003 (c \ue003 \u2013 \ue003 b) \ue003 = \ue003 2, \ue003 determine \ue003 o \ue003 valor \ue003 de \ue003 tg \ue003 (a \ue003 + \ue003 c). \ue003 \ue003 12) Encontre \ue003 o \ue003 valor \ue003 de \ue003 \uf23a \ue74f\ue741\ue74a \ue003\ue754 \ued45 cos \ue755 \uf23b \ueb36 \ued45 \uf23a cos \ue754 \ued45 \ue74f\ue741\ue74a\ue003\ue755 \uf23b \ueb36 , \ue003 sabendo \ue003 que \ue003 x \ue003 + \ue003 y \ue003 = \ue003 30°. \ue003 \ue003 MATEMÁTICA Transformações \ue003 trigonométricas \ue003 2 \ue003\ue003\ue003 2 \ue003 \ue003 www.cursounipre.com.br \ue003 (21) \ue003 4101 \u2010 1013 \ue003 Preparatório \ue003 para \ue003 Concursos \ue003 Militares \ue003 ESFCEX \u2010 ESPCEx \u2010 EsSA \u2010 CHQAO \u2010 AFA \u2010 EP CAr \u2010 EEAER \u2010 EFOMM \u2010 CN \u2010 EN \u2010 Outros \ue003 13) Sabendo \ue003 que \ue003 \ue754\ued45\ue755\ued4c \uec17 \ueb38 , \ue003 encontre \ue003 o \ue003 valor \ue003 de \ue003 \uf23a1 \ued45 \ue750\ue743\ue003\ue754 \uf23b\uf23a1 \ued45 \ue750\ue743\ue003 \ue755\uf23b . \ue003 \ue003 14) Se \ue003 tg \ue003 (x \ue003 + \ue003 y) \ue003 = \ue003 2 \ue003 e \ue003 tg \ue003 y \ue003 = \ue003 1, \ue003 calcule \ue003 tg \ue003 x. \ue003 \ue003 15) Determine \ue003 o \ue003 valor \ue003 de \ue003 \uebe7\uebda \uf23a \ueb38\ueb39°\ueb3e\uebeb \uf23b \ueb3f\uebe7\uebda\ue003\uebeb \ueb35\ueb3e\uebe7\uebda\ue003 \uf23a \ueb38\ueb39°\ueb3e\uebeb \uf23b .\uebe7\uebda\ue003\uebeb . \ue003 \ue003 \ue003 ARCO \ue003 DUPLO \ue003 \ue003 \ue003 \ue003 16) Dado \ue003 \ue74f\ue741\ue74a\ue003\ue754 \ued4c \u221a \ueb37 \ueb36 ,\ue73f \ue74b \ue749 \ue003 0 \ued4f \ue754 \ued4f \uec17 \ueb36 , \ue740\ue741\ue750\ue741\ue74e\ue749\ue745\ue74a\ue741: \ue003 \ue74f\ue741\ue74a\ue0032\ue754 , cos 2\ue754 , \ue750\ue743 \ue0032\ue754 . \ue003 \ue003 17) Sabendo \ue003 que \ue003 \ue74f\ue741\ue74a\ue003\ue754 \ued45 cos \ue754 \ued4c 0,2 , \ue003 determine \ue003 o \ue003 valor \ue003 de \ue003 \ue74f\ue741\ue74a\ue0032\ue754 . \ue003 \ue003 18) Dado \ue003 \ue74f\ue741\ue74a\ue003\ue73d \ued4c \ueb35 \ueb36 \ue003\ue741\ue003\ue74f\ue741\ue74a \ue003\ue73e \ued4c \ueb35 \ueb38 , \ue003 com \ue003 0\ued4f\ue73d , \ue73e \ued4f \uec17 \ueb36 , \ue003 determine \ue003 cos\ue003 \uf23a2\ue73d \ued45 2\ue73e\uf23b . \ue003 \ue003 19) Simplifique \ue003 a \ue003 expressão \ue003 \ueb61\ueb6d\ueb71 \ueb36\uebeb \ueb35\ueb3e\uebe6\uebd8\uebe1\ue003\ueb36\uebeb . \ue003 \ue003 20) Simplifique \ue003 a \ue003 expressão \ue003 \uebe6\uebd8\uebe1\ue003\ueb37\uebd4 \uebe6\uebd8\uebe1\ue003 \uebd4 \ued46 \ueb61\ueb6d\ueb71 \ueb37\uebd4 \ueb61\ueb6d\ueb71 \uebd4 . \ue003 \ue003 21) Se \ue003 tg \ue003 x \ue003 = \ue003 ¼, \ue003 calcule \ue003 tg \ue003 2x. \ue003 \ue003 22) \ue003 Sabendo \ue003 que \ue003 \ue750\ue743\ue003\ue754 \ued4c \ueb37 \ueb39 ,\ue73f \ue74b \ue749 \ue003 0 \ued4f \ue754 \ued4f \uec17 \ueb36 , \ue003 determine \ue003 \ue750\ue743\ue003 \uf240 \uec17 \ueb38 \ued452 \ue754 \uf241 . \ue003 \ue003 23) Sabendo \ue003 que \ue003 \ue74f\ue741\ue74a\ue003\ue754 \ue003. cos \ue754 \ued4c \ueb35 \ueb36 , \ue003 calcule \ue003 o \ue003 valor \ue003 de \ue003 \ue74f\ue741\ue74a \ueb38 \ue754\ued45\ue73f \ue74b \ue74f \ueb38 \ue754 . \ue003 \ue003 24) Simplifique \ue003 a \ue003 expressão \ue003 \uebe6\uebd8\uebe1\ue003\ueb36\uebeb \uebe6\uebd8\uebe1\ue003\uebeb \ued46 \ueb61\ueb6d\ueb71 \ueb36\uebeb \ueb61\ueb6d\ueb71 \uebeb . \ue003 \ue003 25) Sabendo \ue003 que \ue003 sen \ue003 a \ue003 \u2013 \ue003 cos \ue003 a \ue003 = \ue003 2/5, \ue003 calcule \ue003 sen \ue003 2a. \ue003 \ue003 26) Simplifique \ue003 a \ue003 expressão \ue003 abaixo: \ue003 1\ued46\ue750 \ue743 ² \ue754 1\ued45\ue750 \ue743 ² \ue754 \ue003 \ue003 \ue003 \ue003 \ue003 \ue003 \ue003 \ue003 \ue003 \ue003 \ue003\ue003

4 Nota de Aula Transformações Trigonométricas

Matemática

Em Monteiro Lobato

Matemática

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