steve816
  • steve816
Last question of my math homework! Finally it's been a long time! Help me and I'm done with math!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
steve816
  • steve816
Solve please \[\sin(2 \theta) - \cos \theta - 2 \sin \theta + 1 = 0\]
mathmale
  • mathmale
Steve: Didn't hear back from you regarding our discussion of your previously posted question. How did that turn out?
steve816
  • steve816
I figured it out and was right! I substituted the x back with 2 theta and solved.

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steve816
  • steve816
Thanks for the help mathmale :)
mathmale
  • mathmale
All right. What are your thoughts regarding this new post? (You're welcome.)
steve816
  • steve816
This time, I think I can use the double angle formula since there is both sin and cos in the equation?
mathmale
  • mathmale
Chances are that this will work. What have you done so far?
steve816
  • steve816
\[2\sin \theta \cos \theta - \cos \theta - 2\sin \theta + 1 = 0\]
mathmale
  • mathmale
I'm trying to factor this expression. Would you try that on your own, please? Is there a common factor in your equation?
steve816
  • steve816
I think you can distribute the 2sin theta, so now, I have\[2\sin \theta (\cos \theta - 1) - \cos \theta + 1 = 1\]
steve816
  • steve816
Oops, I typed that wrong, I meant = 0
mathmale
  • mathmale
What do you mean by "distribute the 2 sin theta"?
steve816
  • steve816
Sorry, factor out the 2 sin theta
mathmale
  • mathmale
Try it. I've been looking to factor out cos theta, by the way.
steve816
  • steve816
2sinθ(cosθ−1)−cosθ+1=0
mathmale
  • mathmale
Your format looks very similar to mine. Any idea of what to do next? Again I ask you whether your expression has a common factor.
steve816
  • steve816
Hmm, I realize I can cancel out the cosθ−1
mathmale
  • mathmale
with some manupulation you can make cos theta - 1 into 1 - cos theta.
mathmale
  • mathmale
Not "cancel out," Steve, but "factor out." If you drop the factor you've cancelled out, you 'll lose a root or two.
steve816
  • steve816
\[2\sin \theta (\cos \theta - 1) = \cos \theta - 1\] \[2\sin \theta = \frac{ \cos \theta - 1 }{ \cos \theta - 1 }\] \[2\sin \theta = 1\] \[\sin \theta = \frac{ 1 }{ 2 }\]
steve816
  • steve816
I worked out the problem and that is what I got...
steve816
  • steve816
Not sure if it's right though
mathmale
  • mathmale
I've worked thru the same problem in a slightly different way and have come up with 3 solutions on the interval [0,pi]. How would you go about checking the validity of your one solution?
mathmale
  • mathmale
When solving an equation and coming up with a solution, never assume the solution is correct until after you've substituted it back into the original equation and find the equation to be true.
steve816
  • steve816
Oh okay.
steve816
  • steve816
So the two solutions I got are pi/6 and 5pi/6 How did you get 3 solutions?
mathmale
  • mathmale
2sinθ(cosθ−1)−cosθ+1=0 can be re-written as \[2\sin \theta (\cos \theta-1)-( ?? ) = 0\]
mathmale
  • mathmale
Steve, I asked whether you could factor the equation above. Have you been able to do that? If so, you'll end up with 2 factors, each of which you need to set = to zero separately and solve for theta. This is the procedure that got me 3 solutions on [0,pi].
steve816
  • steve816
ohhhh I see what you mean finally!
mathmale
  • mathmale
;)
steve816
  • steve816
Sorry to fail you, but I can't figure out the factors :(
mathmale
  • mathmale
We have \[2\sin \theta(\cos \theta - 1)-\cos \theta +1 = 0\]
mathmale
  • mathmale
and the 2nd half of this equation can be re-written to match that \[\cos \theta -1\]
mathmale
  • mathmale
factor on the left::
steve816
  • steve816
ohhhh, i am so stupid I'm sorry, I got this!
mathmale
  • mathmale
\[2\sin \theta(\cos \theta - 1)-(\cos \theta -1)=0\]
mathmale
  • mathmale
OK with this?
steve816
  • steve816
\[\cos \theta - 1(2\sin \theta - 1) = 0\]
mathmale
  • mathmale
Can you now factor this latest equation?
mathmale
  • mathmale
You can try factoring your own equation also. That's the best way, probably, to determine whether your equation will "work" or not. Mind factoring my last equation now?
mathmale
  • mathmale
My last equation definitely has a common factor. What is that factor?
steve816
  • steve816
I finally got it thanks so much for the 30 minutes of your life :)
mathmale
  • mathmale
It was well spent, Steve. Best of luck to you. Bye for now.

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