## ygarcia 2 years ago Find COS 23pi/6?

1. nelsonjedi

Do you have a calculator?

2. ygarcia

no

3. Abiilovee911

π=180∘

4. ygarcia

so I replace pi with 180?

5. Abiilovee911

yes

6. ygarcia

so it'd be 23*pi divided by 6?

7. Abiilovee911

exactly (:

8. ygarcia

thanks :)

9. Abiilovee911

welcome (:

10. ygarcia

Is 12.03 Right?

11. RolyPoly

cosine of a value cannot be larger than 1...

12. ygarcia

13. RolyPoly

See the graph of cosine:|dw:1389756073553:dw|

14. ygarcia

yes

15. RolyPoly

Maximum of a y=cos x function is 1. Minimum of a y=cosx function is -1

16. ygarcia

so do I need to graph this?

17. nelsonjedi

|dw:1389756066410:dw|

18. RolyPoly

So, you cannot have COS 23pi/6 = 12.03

19. RolyPoly

$\cos\frac{23\pi}{6} = \cos(3(2\pi) + \frac{5\pi}{6}) = \cos\frac{5\pi}{6} = ...?$

20. nelsonjedi

Using the attached drawing where does 23/pi fall?

21. Lethal

Okay sir's let me tell you that. Cos23pi/6 -2pi will give you the same answer

22. ygarcia

idk where 23/pi falls

23. Lethal

Subtract 2pi from it

24. Lethal

The reason you don't know where it falls is becomes you have to do more than one revolution around the circle

25. ygarcia

so i subtract 2pi fom 6?

26. nelsonjedi

2pi = 12pi/6..So 23pi/6-12pi/6 = 11pi/6

27. Lethal

Okay good.

28. nelsonjedi

Are you familiar with the unit circle in trigonometry?

29. Lethal

Now if radians are bothering you we can convert it to degrees.

30. ygarcia

do i need like a specific calculator for this?

31. ygarcia

32. Lethal

You could plug this into your calculator, but if this comes up on a test and you can't use one, you will be screwed.

33. Lethal

11pi/6*180/pi

34. ygarcia

Can you explain how to do it manually?

35. Lethal

That gives us 330 degrees

36. Lethal

Do you know where that is on the unit circle?

37. Lethal

38. ygarcia

yes

39. Lethal

Okay. tell me the coordinates for it.

40. ygarcia

sqrt 2/2, -sqrt 2/2

41. Lethal

Not quite.

42. Lethal

That would be 315 degrees.

43. ygarcia

ummm sqrt 3/2 , -1/2

44. Lethal

yes. sqrt(3)/2, -1/2

45. Lethal

Okay. You should know that Cosx= x

46. Lethal

So what is the value for Cos330?

47. ygarcia

I got -.991...

48. Lethal

Keep this exact. You just gave me the coordinates. and I just told you CosƟ=x

49. Lethal

so what is the exact answer?

50. Lethal

hint: (x,y)

51. Lethal

Use the coordinates you gave me.

52. ygarcia

sqrt 3/2 , -1/2

53. Lethal

Yes and I told you cosƟ=x so what is cos330?

54. ygarcia

I don't get it /.\ I'm sorry

55. ygarcia

when I plug in Cos330 it gives me the decimal I gave you

56. Lethal

|dw:1389757103607:dw|

57. Lethal

Okay also cosƟ=A/H This is the unit circle and the hypotenuse will always be one so basically cosƟ=H what is Cos330?

58. Lethal

ygarcia what calculator are you using btw?

59. ygarcia

I don't have a calculator

60. Lethal

Okay. Well just finish it. Cos330=A. What is A in that triangle? A for adjacent to theta.

61. ygarcia

-1/2?

62. Lethal

|dw:1389757356882:dw|

63. Lethal

No. Adjacent means next to. So what is next to theta that isn't the hypotenuse. -1/2 is opposite.

64. ygarcia

sqrt 3/2

65. Lethal

There you go.

66. ygarcia

so the solution is sqrt 3/2?

67. Lethal

cos330=Sqrt(3)/2

68. Lethal

Yes

69. Lethal

Now let's see if you learned anything. Tell me the sin330 if you know that sinƟ=y

70. ygarcia

-1/2

71. Lethal

Very good. Just use the coordinates you gave me for that degree value. (sqrt(3)/2, -1/2) (x,y) SinƟ=y and the y value for 330 is -1/2 so that's the answer.

72. ygarcia

So Cos= x value and Sin= y value?

73. ygarcia

In reference to the circle

74. Lethal

Yeah. Because in the unit circle the radius is one, that's why it's called a unit circle, one unit. Anytime you have something over 1 It's just whatever the numerator is.

75. ygarcia

Okay, Thanks SO MUCH!!!! I don't fully get it yet but what you explained to me helped A LOT :)

76. Lethal

You're welcome.