anonymous
  • anonymous
Solve: sin3Ө = 0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
arcsin
anonymous
  • anonymous
sin3Ө = sin 0
anonymous
  • anonymous
--> Ө = 0

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anonymous
  • anonymous
i don't get it -.-
anonymous
  • anonymous
Sin 0 =0. 0*any number is 0, so theta would be 0 because 0*3=0
anonymous
  • anonymous
Ok?
anonymous
  • anonymous
0 is not the only solution
anonymous
  • anonymous
Really?
anonymous
  • anonymous
sin(180º)=0...right? sin(360º)=0, sin(-180º)=0
anonymous
  • anonymous
Okk then ?
anonymous
  • anonymous
you have to account for every angle
anonymous
  • anonymous
what is 120 degrees k mean ?
anonymous
  • anonymous
what is "k" anyway ?
anonymous
  • anonymous
k is an integer, any integer
anonymous
  • anonymous
which is how you account for every possible angle theta can be
anonymous
  • anonymous
how did they get 120 degrees k then ?
anonymous
  • anonymous
the answer to this is theta=k*60º, where k is any integer
anonymous
  • anonymous
for example k=1 sin(3*60)=sin(180)=0 k=0 sin(3*0)=sin(0)=0 k=-1 sin(3*-60)=0 k=2 sin(3*2*60)=sin(360)=0
anonymous
  • anonymous
ohh
anonymous
  • anonymous
where did you get the 60 from?
anonymous
  • anonymous
well you could also write 0+k*60º, since we established that the reference angle was 0, but the 0 is unnecessary
anonymous
  • anonymous
so k= either 0,1,2,3 ?
anonymous
  • anonymous
k is ANY integer
anonymous
  • anonymous
the equation will be true whatever the value you plug in for k is
anonymous
  • anonymous
i see
anonymous
  • anonymous
suppose k=500 type in your calculator sin(3*500*60º) you end up with 0
anonymous
  • anonymous
ahh ok
anonymous
  • anonymous
Sin and cos have periodic of 2 pi => sin 3Ө = sin 0 + k 2pi => 3Ө = 0 + k 2pi => Ө = k 2pi / 3 = k 60 degree k = 1, Ө = 60 k = 2, Ө = 120 ... so on

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