anonymous one year ago In △JKL, solve for x. Answer Choices: A) 66.73 B) 74.89 C) 15.44 D) 38.16

1. anonymous

2. Nnesha

$\rm sin \rm \theta = \frac{ opposite }{ hypotenuse }~~~~ \cos \theta = \frac{ adjacent }{ hypotenuse } ~~\tan \theta = \frac{ opposite }{ adjacent }$

3. Nnesha

|dw:1440790508463:dw|

4. Nnesha

which function you should use to find x ?

5. anonymous

The Cos function?

6. Nnesha

which side is adjacent of 27 degree angle ?

7. anonymous

Side KL with the 34 in the middle

8. Nnesha

hmm that would be the opposite side adjacent side would the touch |dw:1440790695818:dw| the angle now look at 27 degree angle

9. Nnesha

kl is adjacent of theta it's a opposite side of 27 degree angle not adj

10. anonymous

Oh, yes. I forgot about the Theta,

11. Nnesha

to find length of x you should know one angle and one side so we would use sin function

12. Nnesha

|dw:1440790850611:dw|

13. anonymous

Wait, how'd you get the Adjacent onto the opposite side? Is it being flipped because of the 27 degrees?

14. Nnesha

different angles different sides

15. anonymous

|dw:1440791024957:dw|

16. Nnesha

JK is n't opposite side of 27 angle

17. Nnesha

yep right solve for x

18. anonymous

Okay, just a second :)

19. anonymous

|dw:1440791173523:dw|

20. anonymous

21. Nnesha

looks good

22. anonymous

Are you sure everything looks right?

23. Nnesha

i know what u r talking about when you put sin(27 degree) into the calculator you will get .45399 so you should round it .45399=.4540

24. Nnesha

|dw:1440791354591:dw|

25. Nnesha

now divide 34/.4540

26. anonymous

Yes, my answer is: 74.889, which will then round to 74.89. Which is B. :)

27. Nnesha

yes :=)

28. anonymous

Could you possibly help me on another question?

29. Nnesha

i'll try

30. anonymous

Okay, would you like it in a different post or here is fine?

31. Nnesha

doesn't matter :=) post that here i'm okay with it

32. anonymous

Find the value of the cot 10° using your calculator. Answer choices: A) 0.176 B) 5.671 C) 0.648 D) 1.542

33. Nnesha

okay use calculator then :D

34. anonymous

How would I type that in though?

35. Nnesha

what is the reciprocal of cot ?

36. anonymous

Hmm, I'm sorry haha, I don't understand this question at all, it wasn't in the lesson I got my notes from..

37. Nnesha

alright then write these down in ur notebook $\large\rm sin \theta = \frac{ 1 }{ \csc \theta }~~~\cos \theta=\frac{ 1 }{ \sec \theta}~~~\tan \theta=\frac{ 1 }{ \cot \theta }=\frac{ \sin \theta}{ \cos \theta}$

38. Nnesha

tan =1/cot or you can say it's equal to sin/cos

39. Nnesha

csc , sec and tan are reciprocal of sin ,cos and cot

40. Nnesha

csc = 1/sin sin =1/csc

41. Nnesha

so if tan = sin /cos cot = ?

42. anonymous

1?

43. Nnesha

what is the reciprocal of sin/cos ?

44. anonymous

tan.

45. Nnesha

okay so cot =1/tan $\huge\rm tan = \frac{ 1 }{ \cot }~~and~~ \cot =\frac{ 1 }{ \tan}$

46. Nnesha

if tan equal sin/cos then replace tan with sin /cos

47. Nnesha

okay so cot =1/tan $\huge\rm \cot =\frac{ 1 }{ \color{red}{\tan}}$$\cot = \frac{ 1 }{ \color{Red}{\frac{ \sin }{ \cos }} }$

48. anonymous

Okay, so you're basically switching them around? With the originally formula.

49. Nnesha

just remember tan =sin/cos

50. Nnesha

yes right

51. Nnesha

now cot = ??

52. Nnesha

$\huge\rm \frac{ 1 }{ \frac{ \sin }{ \cos } } = ?$we can change division to multiplication right

53. anonymous

I'm so confused, I'm understanding pieces but then I'm not.. As I said before, I've never seen this type of question or even demonstration in a lesson I've had.

54. Nnesha

okay let's change that to simple algebra $\huge\rm \frac{ 1 }{ \frac{ a }{ b } }$ how would you simplify it ?

55. anonymous

Multiplying?

56. Nnesha

multiply the numerator by the reciprocal of the bottom fraction $\huge\rm \frac{ 1 }{ \frac{ a }{ b } }=1 \times \frac{b}{a}$

57. anonymous

Why did you change b as the numerator and a as the denominator?

58. Nnesha

ohh so you don't know the definition of reciprocal reciprocal means flip the fraction reciprocal of 2/3 is 3/2

59. Nnesha

so reciprocal of a/b would be b/a so to change division to multiplication you should always multiply the numerator with the reciprocal of the bottom

60. anonymous

Oh okay, I understand.

61. Nnesha

so what is reciprocal of sin/cos ?

62. anonymous

Well, you said reciprocal means to flip the fraction, so would it be cos/sin? Or would it be csc/sec?

63. Nnesha

no just cos /sin

64. Nnesha

tan = sin/cos and cot is reciprocal of tan then cot would be cos/sin

65. Nnesha

$\huge\rm cot \theta= \frac{ \cot \theta }{ \sin \theta }$$\huge\rm cot(10^o)= \frac{ \cos (10)^o }{ \sin(10^o) }$

66. anonymous

Okay, I understand what's going on now. So you'd fill in the 10 degrees with the cot function?

67. Nnesha

another example $\huge\rm \cot (a) =\frac{ \cos(a) }{ \sin(a)}$

68. Nnesha

yes you have to find cot (10 deg) which is not in the calcualtor so you should put cos(10)/sin(10)

69. Nnesha

cot(10) is same as cos(10)/(sin 10)

70. anonymous

It'll give me 5.671. Which is B. I'll have to review those functions more because it's still confusing but I can understand what you're saying. I'll just need to do some more practice.

71. Nnesha

yes practice ,practice and practice you will become trig expert!

72. Nnesha

let me know if you din't understand anything on this post i'll try my best to explain! :=) good luck!