6 + 2 sen x = 1 6 + 2 sen x = 1 6 + 2 sen x = 1 2 cos 2 x + 5 sen x = – 1 2 cos2x + 5 sen x = –1 2 cos 2 x – cos x = 0 2 cos 2 x – cos x = 0 2 cos2x –

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    10-Feb-2015

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<ul><li> Diapositiva 1 </li> <li> 6 + 2 sen x = 1 6 + 2 sen x = 1 6 + 2 sen x = 1 2 cos 2 x + 5 sen x = 1 2 cos2x + 5 sen x = 1 2 cos 2 x cos x = 0 2 cos 2 x cos x = 0 2 cos2x cos x = 0 Clase 74 </li> <li> Diapositiva 2 </li> <li> Identidades fundamentales sen2x + cos2x = 1 sen x cos x tan x = sen x cos x cot x = 1 + tan 2 x = cos 2 x 1 1 + cot 2 x = sen 2 x 1sen2x = 1 cos2xcos2x = 1 sen2x </li> <li> Diapositiva 3 </li> <li> sen(x y) = sen x cos y cos x sen y cos(x y) = cos x cos y sen x sen y tan(x y) = tan x tan y 1 tan x tan y Frmulas de adicin </li> <li> Diapositiva 4 </li> <li> Frmulas del ngulo duplo sen 2x = 2 senx cosx cos 2x = cos2x sen2x tan 2 x = 2 tan x 1 tan 2 x = 1 2 sen 2 x = 2 cos 2 x 1 </li> <li> Diapositiva 5 </li> <li> Resuelve la ecuacin: cos 2x sen x = 0 cos 2x = cos 2 xsen 2 x = 2cos 2 x 1 = 1 2sen 2 x 1 2sen 2 x sen x = 0 2sen 2 x sen x + 1 = 0.(1) 2sen 2 x + sen x 1 = 0 (2 senx 1)(senx + 1) = 0 (0 x 360 o ) 2senx 1 = 0 senx + 1 = 0 </li> <li> Diapositiva 6 </li> <li> sen x = 1212 sen x = 1 x = 30 o I C II C 180 o 30 o =150 o x = 150 o x = 270 o + S = { 30 o ; 150 o ; 270 o } </li> <li> Diapositiva 7 </li> <li> Resuelve la siguiente ecuacin para 0 x 2 para 0 x 2 . cos x(cos2x + 5) + 5sen 2 x = 6 sen 2 x=1cos 2 x cos2x=2cos 2 x1 =12sen 2 x =cos 2 xsen 2 x cos x(2cos 2 x1+5)+5(1cos 2 x)=6 cos x(2cos 2 x+4) + 5 5cos 2 x = 6 2cos 3 x+4cos x+55cos 2 x6=0 2cos 3 x 5cos 2 x + 4cos x 1= 0 </li> <li> Diapositiva 8 </li> <li> 2 5 4 1 1 2 2 3 1 1 0 1)(2cosx 2 (cosx 1)(2cosx 2 3cosx + 1) = 0 1)(cosx 1)= 0 (cosx 1)(2cosx 1)(cosx 1)= 0 cosx = 1 cosx= 1212 x 1 = 0 x 2 = 2 x 4 = 2 3 x 4 = 55 3 x 3 = 3 2cos 3 x 5cos 2 x + 4cos x 1= 0 1)= 0 (cosx 1) 2 (2cosx 1)= 0 </li> <li> Diapositiva 9 </li> <li> Resuelve la ecuacin: tan 2x tan x = 0 tan 2x= 2 tan x 1 tan 2 x 2 tan x 1 tan 2 x tan x = 0. (1 tan 2 x) 0 2 tan x tan x (1 tan 2 x) = 0 2 tan x tan x + tan 3 x = 0 tan 3 x + tan x = 0 tan x (tan 2 x + 1) = 0 Pero: tan 2 x + 1 0 Solo: tan x =0 x = k ; k Z xx 2 +k xx 4 +k 2 kZkZ </li> <li> Diapositiva 10 </li> <li> Para el estudio individual Resuelve : a) b) cos 2x + sen x = 1 sen 2x = sen x S=S=S=S= kkkk 6 5555 6 + 2k + 2k kZkZkZkZ S=S=S=S= kkkk 3 5555 3 kZkZkZkZ C) sen 2x = tan x 4 x = k x = k x = + k 2 kZkZ </li> </ul>

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