Trig help...again :)

Question

haleyelizabeth2017 · Answer

$$2\sin \theta \cos \theta + \sqrt{3} \cos \theta = 0$$

hwyl · Answer

make some attempts

haleyelizabeth2017 · Answer

..I just need help getting started....I don't like direct answers @hwyl, so I'm not asking for one....

hwyl · Answer

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 · Answer

I meant I'm not doing trig for the first time....this is the first time that I am doing this...

haleyelizabeth2017 · Answer

Not all of my trig is like this....not much is actually.

hwyl · Answer

first, clarify if the second term of the problem is $\sqrt{3}~cos \theta $ or $\sqrt{3cos\theta} $

haleyelizabeth2017 · Answer

It's what I put...$$\sqrt {3}~ cos \theta$$

hwyl · Answer

I want to make sure because people make mistakes putting it in latex form.

haleyelizabeth2017 · Answer

:)

hwyl · Answer

is there anything that is factorable?

haleyelizabeth2017 · Answer

What do you mean? O.o

hwyl · Answer

can you factor the left-hand-side (LHS)?

hwyl · Answer

$ab + bc \rightarrow b(a+c) $

hwyl · Answer

in my own opinion, factoring simplifies and does many wonders.

haleyelizabeth2017 · Answer

I'm not quite sure how to factor this....

hwyl · Answer

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 · Answer

So $$cos (2 sin + \sqrt3)?$$

hwyl · Answer

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 · Answer

so find the values where cos is 0?

haleyelizabeth2017 · Answer

and where 2 sin + sqrt 3 equal 0?

haleyelizabeth2017 · Answer

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 · Answer

you're on the right track... you can do on your own

haleyelizabeth2017 · Answer

Wait!  4pi/3?

haleyelizabeth2017 · Answer

and 5pi/3?

hwyl · Answer

easy peachy, isn't it?

haleyelizabeth2017 · Answer

yes! thank you!

hwyl · Answer

you did well and I think you're just going to need a few algebra techniques to get started.