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