6 + 2 sen x = 1
11
6 + 2 sen x = 1 6 + 2 sen x = 1 2 cos 2 cos 2 2 x + 5 sen x = –1 x + 5 sen x = –1 2 cos 2 cos 2 2 x – cos x = 0 x – cos x = 0 Clase 75
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Clase 75. 6 + 2 sen x = 1. Ejercicios sobre Ecuaciones trigonométricas. 2 cos 2 x – cos x = 0. 2 cos 2 x + 5 sen x = –1. cosx. sen x. cos x. Revisión 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
Transcript of 6 + 2 sen x = 1
6 + 2 sen x = 1 6 + 2 sen x = 1 6 + 2 sen x = 1 6 + 2 sen x = 1
2 cos2 cos22x + 5 sen x = x + 5 sen x = –1–12 cos2 cos22x + 5 sen x = x + 5 sen x = –1–1
2 cos2 cos22x – cos x = x – cos x = 00 2 cos2 cos22x – cos x = x – cos x = 00
Clase 75
Revisión del estudio individualRevisión del estudio individual
C)sen 2x = tan xsen 2x = tan x2 senxcosx = sen x
cos x
cosx
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 ó
sen2x =
12
senx = 22
4 x = kx = k ó x
= + k
2kZ
EjercicioEjercicioEjercicioEjercicioResuelve las Resuelve las siguientes ecuaciones:siguientes ecuaciones:Resuelve las Resuelve las siguientes ecuaciones:siguientes ecuaciones:
a) 2 sen 2x cot x – cos 2x = a) 2 sen 2x cot x – cos 2x = 33 cos xcos xa) 2 sen 2x cot x – cos 2x = a) 2 sen 2x cot x – cos 2x = 33 cos xcos xb)b)b)b)
sen xsen xsen xsen x sen 2x cos sen 2x cos x x sen 2x cos sen 2x cos x x = 2 = 2
sensen22xx= 2 = 2 sensen22xx
c) sen 2x = 2 – 2 cos 2xc) sen 2x = 2 – 2 cos 2xc) sen 2x = 2 – 2 cos 2xc) sen 2x = 2 – 2 cos 2x
a) 2 sen 2x cot x – cos 2x = 3 cos x4senx cosxcos
xsenx
–(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 ó cos x = 1
cos x = 12xx11
==
33 + 2k+ 2k ; ;
kkxx22= 2= 2 – –
33
5533==
xx33= = 2k2k
+ 2k+ 2k ; ; kk
b)b)b)b)sen xsen xsen xsen x
sen 2x cos sen 2x cos x x sen 2x cos sen 2x cos x x = 2 = 2
sensen22xx= 2 = 2 sensen22xx
2 senx cosx
cosxsen
x
= 2 sen2x2 cos2
x= 2 sen2x
:: 2 2cos2x – sen2x = 0 cos 2x =
02x2x11 = =
22 + 2k+ 2k 2x2x22
= =
3322 + 2k+ 2k
xx11 = =
44 + k+ k 33
44xx22 = =
+ k+ k
k k
c) sen 2x = 2 – 2 cos 2x
2 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
:: 2 2
senx (2 senx – cosx)= 0 sen x =
0ó ó 2 senx – cosx = 0 x = 180x = 18000kk 2 senx =
cosx 4sen2x = cos2x 4sen2x = 1 – sen2x 5sen2x = 1 sen x
= 1
5
sen x =
5 5
kkZZ
sen x =
5 5
sen x = 0,448
TABLA
xx11 = 26,6 = 26,60 0 + +
36036000kkx2 = (1800 – 26,60) +
3600kxx22 = 153,4 = 153,40 0 + +
36036000kkx3 = (1800 + 26,60) +
3600kxx33 = 206,6 = 206,60 0 + 360+ 36000kkx4 = (3600 – 26,60) +
3600kxx4 4 = 333,4= 333,40 0 + +
36036000kkk k ZZ
0,4478
Resuelve las siguientes ecuacionescon la condición 00o o x x 360 360oo .a) sensen22x + cosx = x + cosx = 00b) cos2x + cos2x = 5sen2xc) cos2x + cosx = cos2x + cosx = 00d) cos2x + sencos2x + sen22xx
1 – senx1 – senx =53
x x = 90o; 270o; 210o; 330o
x x = 30= 30oo; ; 150150o o ;210;210oo ;330 ;330oo
xx=60=60oo; 300; 300oo; 180; 180oo
x x = 90= 90oo; 41,8; 41,8oo; 138,2; 138,2oo
Para el estudio Para el estudio individualindividual
