## DarkBlueChocobo one year ago Help with trig

1. kawii2004

question?

2. DarkBlueChocobo

If tan(theta)>0 and sec(theta)<0 then theta is in which quadrant?

3. Astrophysics

Ever heard of CAST?

4. DarkBlueChocobo

I have not

5. DarkBlueChocobo

But I was thinking if tan = sin/cos then sin and cos were are not negative

6. DarkBlueChocobo

or they are both negative or both positive?

7. Astrophysics

|dw:1443835637183:dw| It's like a quick way to see where the ratios are positive and negative, A represents all positive in that quadrant, S is sin theta, C is cos theta, and T is tan theta. So they are positive in those quadrants where the letter is, and negative in the rest.

8. DarkBlueChocobo

so it would be the 3rd quadrant then?

9. DarkBlueChocobo

since Tan is positive in quadrant 3 ?

10. Astrophysics

Yes, exactly!

11. DarkBlueChocobo

Well thank you for the new method of solving that. That makes everything a lot more easy

12. Astrophysics

It's a pretty handy trick if you don't want to spend a bunch of time on these problems, but know how the ratios work, :)

13. DarkBlueChocobo

Explain how the ratios work? I was thinking if tan is > 0 then sin and cos must be positive in order to get out positive

14. Astrophysics

I mean ratio as in if you have triangles, because $\tan \theta = \frac{ y }{ x }$

15. Astrophysics

$\sin \theta = \frac{ y }{ r }$ $\cos \theta = \frac{ x }{ r }$ $\tan \theta = \frac{ \sin \theta }{ \cos \theta } = \frac{ \frac{ y }{ r } }{ \frac{ x }{ r } } = \frac{ y }{ x }$

16. DarkBlueChocobo

yes but where does that relate to in quadrants?

17. DarkBlueChocobo

i understand the unit circle and stuff I just don't get like what that have to deal with finding it like if it was sin>0 and cos<0 Then you could pinpoint that it was in the 2nd quad cause that's where that is true

18. Astrophysics

Ok lets look at the quadrants |dw:1443836610435:dw| negative*negative = + that's why tan theta is positive

19. Astrophysics

Does that make sense? Or still a bit confused?

20. DarkBlueChocobo

I mean i get that a - * - is a positive. I don't get how it relates to tan though

21. DarkBlueChocobo

oh wait

22. DarkBlueChocobo

you are saying if -y/-x=+yx?

23. DarkBlueChocobo

I would get why that is positive then nevermind

24. Astrophysics

Don't over think, it's not as hard as it seems, remember that these trig functions are all related to right triangles, so that's how we really get these ratios it's just $r = \sqrt{x^2+y^2}$

25. DarkBlueChocobo

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