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cutiecomittee123 one year ago Find sin x and csc y First of all how do use csc on a calculator (if possible) of all how in the world do I set up the equations to solve? I know that sin is opposite over hypotenuse and csc is hypotenuse over opposite

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1. cutiecomittee123

|dw:1441828737649:dw|

2. Nnesha

csc is reciprocal of 1/sin sec is reciprocal of 1/cos cot is reciprocal of 1/tan

3. cutiecomittee123

makes sense. so then to solve for sinx sinx=5/a

4. cutiecomittee123

right?

5. Nnesha

first ) apply the Pythagorean theorem to find 3rd side of right triangle $\huge\rm a^2+b^2=c^2$

6. Nnesha

yes right but first find c (hypotenuse ) let hypotenuse = c

7. cutiecomittee123

okay so 25+49=74

8. cutiecomittee123

and the sqrt of 74 is the hypotenuse

9. Nnesha

yes right that is c^2 but we need c

10. Nnesha

yes right

11. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @cutiecomittee123 makes sense. so then to solve for sinx sinx=5/a $$\color{blue}{\text{End of Quote}}$$ now substitute a for sqrt{74}

12. cutiecomittee123

which is 8.6

13. cutiecomittee123

do i keep it sin(x)=5/sqrt74 or do i simplify

14. cutiecomittee123

okay

15. Nnesha

yes simplify solve for x

16. cutiecomittee123

i get a crazy weird number when i try to calculate that

17. Nnesha

what did you get ? first of all your calculator mode should be on degree 2nd you should take invs sin

18. Nnesha

understand ? ?//

19. cutiecomittee123

okay hold on

20. cutiecomittee123

i get sinx=.0011792563

21. Nnesha

when we have to find an angle then we should use invs sin $x = \sin^{-1} \frac{ 5 }{ 8.6 }$

22. Nnesha

or in other words arcsin http://prntscr.com/8eiznl

23. cutiecomittee123

okay so you just keep it that way, no more simplifying?

24. Nnesha

no use calculator to find x $x = \sin^{-1} \frac{ 5 }{ 8.6 }$

25. cutiecomittee123

alright so x=8.6

26. cutiecomittee123

@Nnesha

27. Nnesha

hmm not x isn't 8.6 the hypotenuse = 8.6

28. Nnesha

|dw:1441834691882:dw|

29. Nnesha

type this into the calculator $\sin^{-1} \frac{ 5 }{ 8.6 }$

30. cutiecomittee123

I did

31. cutiecomittee123

it gave me 8.6

32. cutiecomittee123

wait no it gives me .0011792563

33. Nnesha

hmm not sure how u got that what did you type into the calculator ?

34. cutiecomittee123

i typed x^-1 before then sin(5/8.6)

35. Nnesha

it's sin^{-1} not x^{-1} arcsin =sin^{-1}

36. cutiecomittee123

okay so 98.55

37. cutiecomittee123

that is what i get when i put the inverse second after the other part of the equation

38. Nnesha

on ti-84 calculator ?

39. cutiecomittee123

yeah

40. cutiecomittee123

x^-1 is inverse

41. Nnesha

for that calculator press 2nd-sin then type (5/8.6)

42. cutiecomittee123

Ahh I see, way more acurate answer. x=35.55

43. Nnesha

got it !

44. Nnesha

that's right !

45. cutiecomittee123

okay and then we have to find the csc of y, an you help

46. cutiecomittee123

can*

47. Nnesha

i'll use the fact that all triangles add up to 180 degree so it's right triangle so one angle 90 other angle we just found 35.5 i don't knw why sin (x)= 8.6/7 gives me error on calculator

48. cutiecomittee123

y=54.5

49. Nnesha

yes right

50. cutiecomittee123

alright, i dont know if you still want to help but there are two more and i think i have the hang of it, but it is always nice to have a little help:) find tan c and cot y and find cos x and sec y

51. Nnesha

geez i don't know why it csc y giving me an error anyways $\huge\rm csc( x )=\frac{ 8.6 }{ 7 }$ then find inverse csc

52. cutiecomittee123

there is no csc button

53. Nnesha

with same triangle ?

54. Nnesha

i know but csc = 1/sin so it should be i /sin^{-1}(7/8.6)

55. cutiecomittee123

yes same triangle Okay let me try that

56. cutiecomittee123

so plug in 1/sin(-1) (7/8.6) ????

57. Nnesha

welll i plugged in sin^{-1} (7/8.6) i got 54.48

58. Nnesha

still don't understand anyways move to the next one

59. cutiecomittee123

waiiiiittt, are we still working on the first problem to find csc(y)? because i got the same answer y=54.5 because i just used your advice that there are 180 degrees in a triangle and we already have 90+35.5 and then i subtracted them from 180 and got 54.5 as well. I think that is the right answer

60. Nnesha

yes that's the right answer but i was trying to find how to find csc y without using the fact 180 degree :D

61. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @cutiecomittee123 alright, i dont know if you still want to help but there are two more and i think i have the hang of it, but it is always nice to have a little help:) find tan c and cot y and find cos x and sec y $$\color{blue}{\text{End of Quote}}$$ do you mean tan x ???

62. cutiecomittee123

yes tan x

63. Nnesha

alright try it first remember cot is reciprocal of tan

64. cutiecomittee123

well tan(x)=5/7

65. Nnesha

right solve for x !

66. cutiecomittee123

Okay so I would just multiply by 7 on each side and that makes it 7tan(x)=35

67. Nnesha

well you don't have to multiply by 7 just take the invs tan and then calculator

68. cutiecomittee123

okay so i did 2nd, tan(5/7) and i got 35.54

69. Nnesha

perfect!

70. cutiecomittee123

i did it? is that it lol

71. Nnesha

yes right that's tan x

72. cutiecomittee123

okay so now to find cot y

73. cutiecomittee123

wouldnt it just be cot y = 7/5

74. cutiecomittee123

oh is it just tan(5/7)

75. Nnesha

tan y = what ?

76. cutiecomittee123

well it is inverse tan so i figured you use tan when calculating

77. Nnesha

well you did the opposite tan = opposite over adjacent and cot = adjacent over opposite

78. cutiecomittee123

so you keep it the way it is but just dont take the iverse? sine we took the inverse to find tan x

79. cutiecomittee123

inverse since *

80. Nnesha

guess what i'm so hungry right now i need 2nd opinion on this one i feel like we don't need angle we just write in the form tan x = 7/5 that's it

81. Nnesha

is it just find sin x or solve for x ?

82. Nnesha

or like what is x and y ?

83. Nnesha

$$\color{blue}{\text{Originally Posted by}}$$ @cutiecomittee123 wouldnt it just be cot y = 7/5 $$\color{blue}{\text{End of Quote}}$$ cot y = 5/7 ( adjacent over opposite) so it would be arctan(7/5)

84. Nnesha

ye then cos = adjacent over hyp so same concept with sec just like cot i think ur afk

85. Nnesha

i've to go now.

86. cutiecomittee123

okay i see. Thanks for your help!!!

87. Nnesha

yw

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