anonymous
  • anonymous
Find all solutions in the interval [0, 2π). sin2x + sin x = 0
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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.Sam.
  • .Sam.
Do you know what's the identity for sin2x?
anonymous
  • anonymous
noo i forgot..
.Sam.
  • .Sam.
sin2x=2sinxcosx

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.Sam.
  • .Sam.
So how do you proceed?
anonymous
  • anonymous
2sinx+cosx+sinx=0 right? what do i do next?
.Sam.
  • .Sam.
no, it should be from sin2x + sin x = 0 to 2sinxcosx + sin x =0 right?
anonymous
  • anonymous
ohh yea
.Sam.
  • .Sam.
you should try factoring now
anonymous
  • anonymous
sinx(2cosx+1)=0 is this right? what do i do next? o.O
AravindG
  • AravindG
ya u r right :)
.Sam.
  • .Sam.
yes, now you can let sinx=0 and 2cosx+1=0 then find the x values
AravindG
  • AravindG
equate that to 0 and find x values
anonymous
  • anonymous
so i got cosx=-1/2 how do i find the value of x?
.Sam.
  • .Sam.
well you can do this cosx=-1/2 x=cos^{-1} (-1/2)
anonymous
  • anonymous
so what are all possible values of x? 0 and......what else O.o
AravindG
  • AravindG
@hannahg :) instead of o.O
.Sam.
  • .Sam.
no its not 0
anonymous
  • anonymous
@AravindG :)
.Sam.
  • .Sam.
you calculate cos^(-1) 1/2 first without minus on half you'll get 60 degrees
anonymous
  • anonymous
yes:)
.Sam.
  • .Sam.
then use this chart for cosine |dw:1358873950517:dw| we are looking at the minus side since we got minus half. then 180-60=120 degrees 180+60=240 degrees
AravindG
  • AravindG
@hannahg thats better :)
anonymous
  • anonymous
yes. so all the possible solutions will be pi, pi/3, 2pi/3?
.Sam.
  • .Sam.
you still have sinx=0 to do
anonymous
  • anonymous
yes......! so 0?
.Sam.
  • .Sam.
yes but dont forget about 180
.Sam.
  • .Sam.
|dw:1358874634831:dw|
.Sam.
  • .Sam.
since theta is 0, then you get 180
anonymous
  • anonymous
@.Sam. so what are all solutions in the interval??

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