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## anonymous one year ago If cos theta = -5/13 and sin theta less than 0, what is tan theta?

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1. kittiwitti1

Is this what you're asking?$\text{If }\cos\theta=-\frac{5}{13}\text{ and }\sin\theta\lt0\text{, what is }\tan\theta?$

2. anonymous

yessss

3. kittiwitti1

Okay. First question you ask yourself: which quadrant has negative sines?

4. kittiwitti1

(aka negative "y-values")

5. anonymous

okay um 1 and 3 i think

6. kittiwitti1

Q1 is wrong, but you got Q3. Here's a reference image: http://www.chilimath.com/algebra/intro/point/images/quadrants_1.gif

7. anonymous

i couldnt think without looking so 3 and 4

8. kittiwitti1

But good work nonetheless. =) So now you have narrowed down your options to Q3 and Q4.

9. kittiwitti1

(sorry I need to find some scratch paper)

10. Michele_Laino

hint angle theta has to belongs to the III quadrant: |dw:1435382600490:dw|

11. Michele_Laino

belong*

12. kittiwitti1

Okay yeah what she said. So now we have a triangle in QIII|dw:1435382756655:dw|

13. Michele_Laino

hint: $\Large \sin \theta = - \sqrt {1 - {{\left( { - \frac{5}{{13}}} \right)}^2}} = ...$

14. kittiwitti1

what

15. anonymous

so confusing

16. kittiwitti1

lol I don't remember learning that in high school x_x

17. kittiwitti1

I thought there were two answers to this question tbh

18. Michele_Laino

it is the value of the associated function sin(\theta): $\Large \sin \theta = - \sqrt {1 - {{\left( {\cos \theta } \right)}^2}}$

19. kittiwitti1

On second thought I think I'll let her explain because I just confused myself. :v

20. anonymous

answer choices a. 12/5 b.13/5 c.-12/5 d.square root of 194/5

21. Michele_Laino

hint: next steps: $\Large \begin{gathered} \sin \theta = - \sqrt {1 - {{\left( { - \frac{5}{{13}}} \right)}^2}} = - \sqrt {1 - \frac{{25}}{{169}}} = \hfill \\ \hfill \\ = - \sqrt {\frac{{144}}{{169}}} = - \frac{{12}}{{13}} \hfill \\ \end{gathered}$

22. anonymous

still so confused

23. anonymous

in case you guys don't get where he got that radical from, he's using the identity $$\sin^2\theta+\cos^2\theta=1$$

24. Michele_Laino

hint: so we can write: $\Large \tan \theta = \frac{{\sin \theta }}{{\cos \theta }} = \frac{{ - \frac{{12}}{{13}}}}{{ - \frac{5}{{13}}}} = ...?$

25. kittiwitti1

Oh I mostly get it but I was multitasking sorry xD so I decided to leave the problem to someone who could focus their whole effort into helping

26. Michele_Laino

please, complete my computation above @brandijeannnn

27. anonymous

12/5

28. Michele_Laino

that's right!

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