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Jamierox4ev3r

  • one year ago

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  1. Jamierox4ev3r
    • one year ago
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    Give me a second to type the equation, thanks :)

  2. Jamierox4ev3r
    • one year ago
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    Solve: \[2\tan ^{2}\theta \sin \theta - \tan ^{2}\theta=0\] for all values in [0, 360] <---degrees

  3. Jamierox4ev3r
    • one year ago
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    @ganeshie8 any ideas?

  4. ganeshie8
    • one year ago
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    it seems \(\tan^2\theta\) is common in both the terms you may start by factoring it out

  5. Jamierox4ev3r
    • one year ago
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    Alright. So that would be \( \tan( 2\tan \theta \sin \theta-\tan \theta )\) right?

  6. ganeshie8
    • one year ago
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    pull out the entire \(\tan^2\theta\)

  7. Jamierox4ev3r
    • one year ago
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    the entire thing? then that would leave you with.. just sine I believe. So \(\tan^{2} \theta (2\sin \theta-\theta)\)

  8. ganeshie8
    • one year ago
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    wait a sec, \(\tan^{2} \theta (2\sin \theta-\color{Red}{\theta})\) are you really sure that \(\color{Red}{\theta}\) stays back there ?

  9. Jamierox4ev3r
    • one year ago
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    wait... no it wouldn't. whoops xD

  10. ganeshie8
    • one year ago
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    \(\tan^2\theta\) is ONE SINGLE thing \(\tan^2\) and \(\theta\) are not two pieces

  11. Jamierox4ev3r
    • one year ago
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    ^ yes I recall that now. But wouldn't something have to stay there?

  12. Jamierox4ev3r
    • one year ago
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    oh wait. wouldn't it just be -1?

  13. ganeshie8
    • one year ago
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    good, please fix it also what happened to \(= 0\)

  14. Jamierox4ev3r
    • one year ago
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    oh it's still there, I just lopped it off. So as of now, this is where we are. \(\tan^{2} \theta (2\sin \theta-1)=0\)

  15. ganeshie8
    • one year ago
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    looks good! what are you going to do next

  16. Jamierox4ev3r
    • one year ago
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    I'm not sure....seems to me like there is a trigonometric identity somewhere in there perhaps.

  17. ganeshie8
    • one year ago
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    Easy, actually we're almost done! all we need to know is the "zero product property"

  18. ganeshie8
    • one year ago
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    |dw:1441068917025:dw|

  19. ganeshie8
    • one year ago
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    so far we have : \(\color{red}{\tan^{2} \theta} \color{blue}{(2\sin \theta-1)}=0\) By zero product property, \(\color{red}{\tan^2\theta}=0\) or \(\color{blue}{2\sin\theta-1}=0\) solve each of them separately using unit circle

  20. Jamierox4ev3r
    • one year ago
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    so we could set either one to zero. And solve for theta \((\theta)\)

  21. ganeshie8
    • one year ago
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    Exactly! thats what zero product property tells us

  22. Jamierox4ev3r
    • one year ago
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    wow. that actually makes so much sense. Alright, so let me solve each separately and I'll be back with you on what I got

  23. ganeshie8
    • one year ago
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    take ur time you may have to use unit circle as you're asked to find all the solutions between 0 and 360

  24. Jamierox4ev3r
    • one year ago
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    Noted.

  25. Jamierox4ev3r
    • one year ago
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    Alright. So I got that \(\Large\sin \theta = \frac{1}{2}\) So from that, I found that \(\Large\theta = 30 (degrees), 150 (degrees)\)

  26. Jamierox4ev3r
    • one year ago
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    I wasn't as sure for \(\tan \theta\), but I think that \(\Large\tan \theta =0\) and from that, wouldn't \(\Large\theta = 0 (degrees)\) ?? **not sure**

  27. ganeshie8
    • one year ago
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    Excellent! \(\tan\theta=0\) should give you 3 solutions

  28. ganeshie8
    • one year ago
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    il give a hint : \(\tan\theta = \tan(\theta+180)\)

  29. Jamierox4ev3r
    • one year ago
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    oh wait i think i see. 90 degrees would be undefined

  30. ganeshie8
    • one year ago
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    In other words : adding 180 to the angle wont change the value of \(\tan(\theta)\)

  31. Jamierox4ev3r
    • one year ago
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    right.

  32. Jamierox4ev3r
    • one year ago
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    I get that.

  33. ganeshie8
    • one year ago
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    \(\tan\theta=0\) \(\implies \theta = \{0,\pm 180,\pm 360,\pm540,\ldots\}\) since you want the solutions between 0 and 360 you just pick \(0,180,360\)

  34. Jamierox4ev3r
    • one year ago
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    oh and btw, I can include 0 degrees, but not 360. I was supposed to write the problem like [0,360) instead of [0,360]. So technically, for this problem, there are only two solutions that come from \(\tan \theta =0\)

  35. ganeshie8
    • one year ago
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    Oh then you're absolutely right!

  36. Jamierox4ev3r
    • one year ago
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    alright, so in total, all the solutions are 0, 30, 150, and 180! (all in degrees) oh my goodness, thank you so much! This review material was so distant in my memory, until you came along of course. Your patience is outstanding, thank you

  37. ganeshie8
    • one year ago
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    np your patience is outstanding too! keep it up :)

  38. Jamierox4ev3r
    • one year ago
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    d'aw you flatter me :')

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