lilsis76 Group Title Determine all of the solutions in the interval 0< Theta < 360. cos(Q/2) = 1/2 Q is theta one year ago one year ago

1. lilsis76 Group Title

@zepdrix

2. Raja99 Group Title

120,360

3. anikay Group Title

oh my, beaten to the punch gj

4. lilsis76 Group Title

haha okay so then hmmm

5. lilsis76 Group Title

how would that be? @zepdrix i dont get it. i see cos Q/2 that would mean cos = 1/2 right? and if its positive it would be in the 1st and 4th Quadrant?

6. anikay Group Title

well, now that I think about it, I think raja might be wrong

7. anikay Group Title

it should have 4 solutions right?

8. lilsis76 Group Title

im not sure, it just says to determine all solutions in the interval 0-->360

9. Raja99 Group Title

yes!

10. zepdrix Group Title

Using Q? Oooo I like that :) I'm always having trouble finding a suitable letter for theta in text, that works quite well XD

11. anikay Group Title

^concur

12. lilsis76 Group Title

lol ya, i got tired ofputting theata.

13. Raja99 Group Title

30

14. lilsis76 Group Title

okay is it 60 and 300 degrees?

15. Raja99 Group Title

no tetha is 30

16. zepdrix Group Title

$\large \cos(\theta/2)=\frac{1}{2}$We need to solve for theta, which involves a little more than just finding a special angle. If it helps, think of the ENTIRE inside of cosine as an angle, like this,$\large \cos(\phi)=\frac{1}{2}$Where is phi =1/2? Which special angles?

17. anikay Group Title

look, as I solve it, it's $\theta=2\cos^{-1} (1/2)$

18. anikay Group Title

the thing is, that only gives you 120. but it's a good starting point

19. lilsis76 Group Title

mmmmm... okay, well first. special angles is like 45-45-90, and 30-60-90, right?

20. zepdrix Group Title

The special angles are 0,30, 45, 60, 90 In radians 0, pi/6, pi/4, pi/3, pi/2 and so on... Remember those? :) We're not talking about special triangles :D Special angles on the unit circle.

21. lilsis76 Group Title

oh....okay i gotcha now on special angles. lol im totaly flipped around in this class

22. lilsis76 Group Title

okay then so..cosQ/2 = 1/2 right? so cos would be a positive

23. anikay Group Title

I think 120 is it.....

24. zepdrix Group Title

yes the cosine is producing a positive value, so we're concerned with angles in the 1st and 4th quadrant right? :O Cuz that's where cosine is positive.

25. lilsis76 Group Title

yes :) 1st and 4th

26. anikay Group Title

so, if we find the reference angle, then what would the two angles be?

27. lilsis76 Group Title

mmm....pi/3 and 5pi/6?

28. anikay Group Title

yes to the first, the last, not so much, that's in the second quadrant

29. anikay Group Title

or am I failing?

30. zepdrix Group Title

lol :) They should both either be /6 or /3 :D you should get similar angles in that sense. Also, the domain of theta was given to us in DEGREES. let's try to keep it in degrees :)

31. lilsis76 Group Title

oh. haha i mean 5pi/3

32. anikay Group Title

With zepdrix, but you are right

33. lilsis76 Group Title

so the second answer would be 5pi/3?

34. anikay Group Title

but, the problem is, we need that angle to be doubled to match our equation of theta/2

35. lilsis76 Group Title

hmmm...ok okkay, so doubled from pi/3, so pi/3 and 5pi/6?

36. anikay Group Title

uh, lets throw this back to degrees shall we? pi/3 = 60 and 5pi/3 = 300

37. lilsis76 Group Title

DANG! haha okay, so first we have 60 and u said to double it, so that would be 120, 120 would be.....that 5pi/6

38. anikay Group Title

no, 5pi/6 = 150 degrees

39. lilsis76 Group Title

haha shoot what am i doing wrong

40. anikay Group Title

here's a tip. every pi/6 = 30 degrees

41. lilsis76 Group Title

pi/6 pi/4 pi/3 pi/2 4pi/6div by 2 = 2pi/3 OH!.....haha okay so pi/3 and 2 pi/3???

42. anikay Group Title

just plug those into your original equation and see what you get :P

43. lilsis76 Group Title

i dont have an equatioN haha says determine all of the solutions in the interval 0< Q<360 cos(Q/2) = 1/2 so the answers would be pi/3 and 2pi/3? right?

44. lilsis76 Group Title

@anikay

45. lilsis76 Group Title

@zepdrix is it pi/3 and 2pi/3?

46. zepdrix Group Title

If the problem had been,$\large \cos\left(\theta\right)=\frac{1}{2}$We would have concluded that,$\large \theta=\quad 60^o,\quad 300^o$ But our problem involved Q/2, not Q. Giving us,$\large \cos\left(\frac{\theta}{2}\right)=\frac{1}{2}$ $\frac{\theta}{2}=\quad 60^o,\quad 300^o$ From here, if we multiply both sides by 2, we can solve for Q.

47. anikay Group Title

yup^

48. zepdrix Group Title

I'm a little confused why you're messing with the radians :C They're a little more confusing to work with. The domain of Q was GIVEN to us in DEGREES. So let's work in degrees! :D

49. lilsis76 Group Title

AH! so i was right?! the 60 and 300?!

50. zepdrix Group Title

$\large \theta=\quad 120^o, \quad 600^o$

51. anikay Group Title

and since we're going only to 360?

52. anikay Group Title

(radians are easier imo but degrees work k)

53. lilsis76 Group Title

AH!!! im so lost haha

54. zepdrix Group Title

aw :D

55. anikay Group Title

its almost like you're my lilsis or somethin xD

56. lilsis76 Group Title

lol,

57. lilsis76 Group Title

okay so i get the 1/2 and that is in the first quad giving me 60 degrees right?

58. lilsis76 Group Title

@anikay

59. anikay Group Title

yes, and the 300

60. lilsis76 Group Title

okay, how can i figure out the 300?!

61. anikay Group Title

it's a reference angle of 60

62. lilsis76 Group Title

yes it is a ref angle 60

63. lilsis76 Group Title

WAIT!!! 300 cuz its cos 1.2, sin - sqrt3 /2 ?!

64. lilsis76 Group Title

right?! dang i think im slow

65. anikay Group Title

uh

66. lilsis76 Group Title

haha did i do it right?!

67. anikay Group Title

yes

68. lilsis76 Group Title

YAY!!!! > . < THANK YOU SO MUCH!!! ugh....

69. anikay Group Title

however, you have to double those and since you only go to 360, 120 is your only answer

70. phi Group Title

sometimes sketching the curve is helpful |dw:1355239813847:dw|

71. anikay Group Title

agreed, but my calculator is dead xD