anonymous
  • anonymous
3sin3x-√(3)cos3x=-3 i got to a point where sin(3x+150)=√(3)/2 what's next?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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primeralph
  • primeralph
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jdoe0001
  • jdoe0001
next as primeralph suggested, is ARCSINE both sides
anonymous
  • anonymous
i got x=-30+120k and x=-10+120k but the book says 110+120k and 90+120k what am i doing wrong?

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primeralph
  • primeralph
What's the k for?
anonymous
  • anonymous
k can be 0,1,2,3... it represents the periodicity (repetition) of the angle
primeralph
  • primeralph
Okay, are you using degrees or rad?
anonymous
  • anonymous
deg
jdoe0001
  • jdoe0001
I believe the "k" only applies when you're dealing with an angle notation, once you get the value for the angle, any other reference angle will be the same exact value anyway, and "k" becomes irrelevant
primeralph
  • primeralph
@athalef I see what you mean. I think the problem is from your earlier work. Start over.
RadEn
  • RadEn
3sin3x-√(3)cos3x=-3 given a = 3 and b = - sqrt(3) so, k = sqrt(a^2 + b^2) = sqrt(3^2 + (-sqrt(3))^2) = sqrt(12) = 2 sqrt(3) and tanθ =a/b = 3/-sqrt(3) = -sqrt(3) and we knowed that θ in the second quadrant, therefore θ = 120 degrees know, the equation above can rewrite : k cos(3x - θ) = -3 2 sqrt(3)cos(3x - 120) = -3 cos(3x - 120) = -3/2sqrt(3) = -1/2 sqrt(3) case I : cos(3x - 120) = -1/2 sqrt(3) cos(3x - 120) = cos(k360 +- 150) solve for x case II : cos(3x - 120) = -1/2 sqrt(3) cos(3x - 120) = cos(k360 +- 210) solve for x
anonymous
  • anonymous
\[put r \cos \theta=3,r \sin \theta=\sqrt{3} \] square and add, \[r ^{2}=12,r=2\sqrt{3},dividing \tan \theta=\frac{ 1 }{ \sqrt{3} }=\frac{\frac{ 1 }{ 2 } }{\frac{ \sqrt{3}}{ 2 } }\] \[=\frac{ \sin 30 }{ \cos30 }=\tan 30\] \[\theta=30\] \[r \cos \theta \sin 3x-r \sin \theta \cos 3x=-3\] \[r \sin \left( 3x-\theta \right)=-3,2\sqrt{3}\sin \left( 3x-\theta \right)=-3\] \[\sin \left( 3x-\theta \right)=-\frac{ \sqrt{3} }{2 }=-\sin 60=\sin \left( 180+60 \right),\sin \left( 360-60 \right)\] \[3x-\theta=240,300,3x-30=240,300,3x=270,330,x=90,110\]

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