## SugarRainbow 3 years ago if cos 0<0 and tan 0 >0 then in which quadrant does 0 lie? (0=beta IDK how to do the symbol on here)

1. hartnn

|dw:1349413466539:dw| the ratios mentioned are positive in that quadrant.

2. SugarRainbow

oh so its in quadrant 1?

3. hartnn

in quadrant 1 ALL are positive, your question requires, tan to be negaive, so its not in 1st quadrant

4. hartnn

*sorry, cos to be negative

5. hartnn

from the diagram, in which quadrant you find tan to be positive ?

6. SugarRainbow

oh so 4?

7. hartnn

|dw:1349413799469:dw|

8. SugarRainbow

uh tan is positive in idk i looking at my unit circle and where tan is on your diagram its negative unless its in q1

9. ByteMe

cos (beta) < 0 means beta is in QII, QIII tan (beta) > 0 means beta is in QIII, QI where does beta have to be to meet these two requirements?

10. hartnn

|dw:1349413873008:dw|

11. SugarRainbow

but tan is x right? wait can i even reate this to this|dw:1349413939970:dw|

12. hartnn

that circle has co=ordinates of cos and sine so now you know the signs of cos and sine can u find out sign of tan using that, in each quadrant ?

13. SugarRainbow

oh wait tan = sin/cos/45 in which yes that part is positive so its in q3!!!!!

14. SugarRainbow

hey just for note taking is the cot negative then?

15. hartnn

when tan is positive cot = 1/ tan is also positive

16. SugarRainbow

so is tan ever negative then cat is too

17. hartnn

tan is negative when only one of sin or cos is negative, that is in 2nd and 4th quadrant

18. SugarRainbow

and in the all part they're alll only positive right

19. hartnn

yes. in 1st quadrant all ratios are positive

20. akash_809

just a way, i used to remember above diagaram, Add , Sugar, To ,Coffe...

21. SugarRainbow

okay then in q2 and q4 then cot is - yes?

22. hartnn

yes.

23. SugarRainbow

okay then sin is + in q2 and - in q 3 and 4?

24. hartnn

yes, you are reading it correctly :)

25. SugarRainbow

26. SugarRainbow

to akash_809 I see wat you did there

27. hartnn

since sec = 1/cos sign of sec is same as sign of cos everywhere

28. SugarRainbow

oh i meant csc

29. hartnn

csc x =1/ sin x sign of csc is same as sign of sin everywhere

30. SugarRainbow

oh wait cos is + in q4 and - in q 2 and 3 correct?

31. hartnn

yes.

32. SugarRainbow

okay now can we do the next question

33. hartnn

u can use Add sugar to coffee or All silver tea cups to remember that diagram. or you could make one on your own.

34. hartnn

35. SugarRainbow

lol

36. SugarRainbow

yeah i gots it now the all suckers take crap is the ones that are the only ones positive in their quadrant (except q1 where they're all positive)

37. SugarRainbow

okay next question how would you find exact value of 5pi/3?

38. hartnn

5pi/3 ? in degrees ? or some ratio of 5pi/3 ? like sin 5pi/3

39. SugarRainbow

umm it just says "the exact value of csc (5pi/3) (oops i guess i forgot the ratio part sorry)

40. hartnn

u need to use some of trignometry identities. first can u find sin (5pi/3) because csc =1/ sin

41. cansdy21356

i need help . The image below shows two parallel lines cut by a transversal. What is the value of a? two vertical lines cut with a transversal, the angle below and to the right of where the transversal intersects the left line is labeled 2 a plus 3 degrees, and the angle above and to the right of where the transversal intersects the right line is labeled a degrees

42. SugarRainbow

yes its -square root 3/2 and you would multiply by radical 3 to get -2sqrt3/3!!!!

43. hartnn

umm, - root 3 / 2 ... why do u need to multiply by radical ? sin 5pi/6 = - root 3 /2 csc 5 pi/6 = -2/ root 3 here, you will multiply by radical 3 to get csc 5pi/6 = -2sqrt3/3

44. SugarRainbow

yeah that's what i got?

45. hartnn

then you are correct :)

46. SugarRainbow

okay last question how would you horizontally shift y=4 sin (beta-80)

47. SugarRainbow

oh yeah and this question says determine the exact values of the 6 trigonometric functios of an angle in standard position whose terminal side passes through the point (-1,3) and for tan i got -1/3 and cot i got 3/3 and she said its wrong so was i supposed to do...

48. SugarRainbow

-1/sqrt10 then multiply by sqrt 10 to get -1sqrt10/10?

49. hartnn

sorry, can u post this as a new question, i need to go :(