## haleyelizabeth2017 one year ago Trig help...again :)

1. haleyelizabeth2017

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

2. anonymous

make some attempts

3. haleyelizabeth2017

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

4. anonymous

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?

5. haleyelizabeth2017

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

6. haleyelizabeth2017

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

7. anonymous

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

8. haleyelizabeth2017

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

9. anonymous

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

10. haleyelizabeth2017

:)

11. anonymous

is there anything that is factorable?

12. haleyelizabeth2017

What do you mean? O.o

13. anonymous

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

14. anonymous

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

15. anonymous

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

16. haleyelizabeth2017

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

17. anonymous

well look at the example I showed you look for something common in the first and second term. from what I can see, $$cos ~\theta$$

18. haleyelizabeth2017

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

19. anonymous

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.

20. haleyelizabeth2017

so find the values where cos is 0?

21. haleyelizabeth2017

and where 2 sin + sqrt 3 equal 0?

22. 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....

23. anonymous

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

24. haleyelizabeth2017

Wait! 4pi/3?

25. haleyelizabeth2017

and 5pi/3?

26. anonymous

easy peachy, isn't it?

27. haleyelizabeth2017

yes! thank you!

28. anonymous

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