## anonymous one year ago If tan theta =12/5 and cos theta =-5/13, then what is sin theta?

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1. anonymous

@peachpi

2. Michele_Laino

hint: $\tan \theta = \frac{{\sin \theta }}{{\cos \theta }}$

3. anonymous

i am confused

4. anonymous

@Michele_Laino totally missed that. Much simpler than what I was going to do

5. anonymous

how do i go on from there

6. anonymous

what @Michele_Laino has posted is an identity for tan. From here you plug in your numbers and solve for sin Θ

7. Michele_Laino

8. anonymous

the answer i got is 12/13

9. anonymous

im not sure what i did, is that correct

10. anonymous

you should have gotten a negative number

11. UsukiDoll

you're missing a negative sign.

12. anonymous

so the answer would be -12/13???

13. anonymous

yes

14. anonymous

i just did the question again and got -5/13..... i am overthinking the problem i think

15. anonymous

16. anonymous

|dw:1436185957944:dw|

17. UsukiDoll

$\tan(\theta)\cos(\theta) = \sin(\theta)$ since we are given 12/5 for tangent and -5/13 for cosine $\frac{12}{5}(\frac{-5}{13}) = \sin(\theta)$ the 5's cancel and you are left with -12/13

18. UsukiDoll

wow this is the first time I've done like this to be honest xD

19. anonymous

thank you guys!!!!!!

20. anonymous

me too. I usually draw it and use the quadrants

21. anonymous

you're welcome

22. UsukiDoll

same... since sin was negative and cos was negative, I'm assuming that we were in quadrant 3 because tangent is positive.

23. anonymous

yes. I was dutifully drawing a picture when michele came in and blew my mind xD

24. UsukiDoll

hmmm the triangle method would've worked too.. because tangent = opposite/adjacent = 12/5 and cosine = adjacent/hypotenuse =- 5/13 |dw:1436186175987:dw| except we have to respect the fact that since cosine is negative we are placed in one of the four quadrants.

25. UsukiDoll

yeah I remember have those problems with the triangles like this and the textbook was like one of them is negative so which quadrant are we

26. UsukiDoll

sorry my typing not working tonight xD but quadrant three is 180 degrees-270 degrees and only tangent is positive.