haleyelizabeth2017
  • haleyelizabeth2017
Trig help...again :)
Mathematics
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haleyelizabeth2017
  • haleyelizabeth2017
Trig help...again :)
Mathematics
katieb
  • katieb
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haleyelizabeth2017
  • haleyelizabeth2017
\[2\sin \theta \cos \theta + \sqrt{3} \cos \theta = 0\]
hwyl
  • hwyl
make some attempts
haleyelizabeth2017
  • haleyelizabeth2017
..I just need help getting started....I don't like direct answers @hwyl, so I'm not asking for one....

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hwyl
  • hwyl
like what kind of help to get started? you said "again," so it means you are not doing this for the first time. What part of the problem you don't understand?
haleyelizabeth2017
  • haleyelizabeth2017
I meant I'm not doing trig for the first time....this is the first time that I am doing this...
haleyelizabeth2017
  • haleyelizabeth2017
Not all of my trig is like this....not much is actually.
hwyl
  • hwyl
first, clarify if the second term of the problem is \(\sqrt{3}~cos \theta \) or \(\sqrt{3cos\theta} \)
haleyelizabeth2017
  • haleyelizabeth2017
It's what I put...\[\sqrt {3}~ cos \theta\]
hwyl
  • hwyl
I want to make sure because people make mistakes putting it in latex form.
haleyelizabeth2017
  • haleyelizabeth2017
:)
hwyl
  • hwyl
is there anything that is factorable?
haleyelizabeth2017
  • haleyelizabeth2017
What do you mean? O.o
hwyl
  • hwyl
can you factor the left-hand-side (LHS)?
hwyl
  • hwyl
\(ab + bc \rightarrow b(a+c) \)
hwyl
  • hwyl
in my own opinion, factoring simplifies and does many wonders.
haleyelizabeth2017
  • haleyelizabeth2017
I'm not quite sure how to factor this....
hwyl
  • hwyl
well look at the example I showed you look for something common in the first and second term. from what I can see, \(cos ~\theta \)
haleyelizabeth2017
  • haleyelizabeth2017
So \[cos (2 sin + \sqrt3)?\]
hwyl
  • hwyl
perfect! now complete the form \(ab + bc = 0 \rightarrow b(a+c) = 0 \rightarrow b =0, ~ a+c = 0 \) what we are basically looking for are the values when the curves or lines passes through the x-axis, which we call the ZEROES.
haleyelizabeth2017
  • haleyelizabeth2017
so find the values where cos is 0?
haleyelizabeth2017
  • haleyelizabeth2017
and where 2 sin + sqrt 3 equal 0?
haleyelizabeth2017
  • haleyelizabeth2017
if so, then 2 of them are pi/2 and 3pi/2. How do I find the other ones? I'm not quite sure how to do it with the 2....
hwyl
  • hwyl
you're on the right track... you can do on your own
haleyelizabeth2017
  • haleyelizabeth2017
Wait! 4pi/3?
haleyelizabeth2017
  • haleyelizabeth2017
and 5pi/3?
hwyl
  • hwyl
easy peachy, isn't it?
haleyelizabeth2017
  • haleyelizabeth2017
yes! thank you!
hwyl
  • hwyl
you did well and I think you're just going to need a few algebra techniques to get started.

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