6 + 2 sen x = 1

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    03-Jan-2016

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Clase 75. 6 + 2 sen x = 1. Ejercicios sobre Ecuaciones trigonomtricas. 2 cos 2 x cos x = 0. 2 cos 2 x + 5 sen x = 1. cosx. sen x. cos x. Revisin del estudio individual. C). sen 2x = tan x. 2 senxcosx =. 2 senxcos 2 x = senx. 2 senx (1 sen 2 x) sen x = 0. - PowerPoint PPT Presentation

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

  • Revisin del estudio individualC)sen 2x = tan x2 senxcosx =2 senxcos2x = senx2 senx (1 sen2x) sen x = 0 2 senx 2 sen3x sen x = 0 2 sen3x sen x = 0 senx(2sen2x 1) = 0

  • senx(2sen2x 1) = 0 sen x = 0 sen2x = kZ

  • EjercicioResuelve las siguientes ecuaciones:a) 2 sen 2x cot x cos 2x = 3 cos xb)sen x sen 2x cos x = 2 sen2xc) sen 2x = 2 2 cos 2x

  • a) 2 sen 2x cot x cos 2x = 3 cos x4senx cosx(2cos2x 1) = 3 cos x 4 cos2x 2 cos2x + 1 = 3 cos x2 cos2x 3 cos x + 1 = 0(2 cos x 1)(cos x 1) = 0 cos x = 1cos x = x1=+ 2k ; kx2= 2 x3= 2k + 2k ; k

  • b)sen x sen 2x cos x = 2 sen2x2 senx cosxcosxsen x= 2 sen2x2 cos2 x= 2 sen2xcos2x sen2x = 0 cos 2x = 02x1 = + 2k2x2 = + 2kk

  • c) sen 2x = 2 2 cos 2x2 senx cosx = 2 (1 cos2x) senx cosx = [1 (1 2sen2x)] senx cosx = [1 1 + 2sen2x)] 2 sen2x senx cosx = 2 sen2x senx cosx = 0 senx (2 senx cosx) = 0

  • senx (2 senx cosx)= 0 sen x = 0 2 senx cosx = 0 x = 1800k2 senx = cosx 4sen2x = cos2x 4sen2x = 1 sen2x 5sen2x = 1kZ

  • sen x = 0,448TABLAx1 = 26,60 + 3600kx2 = (1800 26,60) + 3600kx2 = 153,40 + 3600kx3 = (1800 + 26,60) + 3600kx3 = 206,60 + 3600kx4 = (3600 26,60) + 3600kx4 = 333,40 + 3600kk Z

  • 0,4478

  • Resuelve las siguientes ecuacionescon la condicin 0o x 360o .a) sen2x + cosx = 0b) cos2x + cos2x = 5sen2xc) cos2x + cosx = 0d) x = 90o; 270o; 210o; 330ox = 30o; 150o ;210o ;330ox=60o; 300o; 180o x = 90o; 41,8o; 138,2oPara el estudio individual

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