## anonymous one year ago Find the values of the six trigonometric functions for angle Θ. https://my.dcdal.org/pluginfile.php/3759/question/questiontext/10967/1/5436/1.jpg

1. anonymous

2. anonymous

I can't access it because it directs me to the log in page of the website.

3. anonymous

let me try it another way

4. anonymous

|dw:1438578342154:dw|

5. anonymous

this is what it looks like

6. anonymous

i am trying it and i got 0.625 for the sin.

7. anonymous

How did you get 0.625? What did you do?

8. anonymous

These are the 6 trigonometric functions btw. |dw:1438578372182:dw|

9. anonymous

figured up the hypotenuse at 19.2 and then i took the opposite which is 12 and divided it by the hypotenuse.

10. anonymous

11. anonymous

wasn't specified

12. anonymous

so i just did it in decimals.

13. anonymous

I'd suggest you'll write in fractions. :)

14. anonymous

okay so should i convert it over?

15. anonymous

usually if its not how the computer wants it my teacher fixes it but i can always do it in fractions.

16. anonymous

You're right that the hypotenuse is 19.2, but let's convert it with radicals :) So the hypotenuse is |dw:1438578691977:dw|

17. anonymous

okay.

18. anonymous

It is always easier to convert from fractions to decimals than from decimals to fractions. XD

19. anonymous

i noticed lol

20. anonymous

Did you see the image above? About the six trigo functions? Just apply it.

21. anonymous

yes

22. anonymous

Let's start with sine. $\huge sine=\frac{ opposite }{ hypotenuse }$ We know that the opposite=12, adjacent=15, and hypotenuse=3 sqrt 41. So what would sine be?

23. anonymous

Still there?

24. anonymous

yeah trying to figure it out

25. anonymous

Hmmm don't use your calculator. Just plug in the numbers then that's it. Let this be in fraction form.

26. anonymous

im not using a calculator I'm just that bad at math

27. anonymous

12/3sqrt41

28. anonymous

Correct.

29. anonymous

thats how i do it?

30. anonymous

that easy?

31. anonymous

Yes. :)

32. anonymous

theres no way its that easy

33. anonymous

But... you need to rationalize it because the denominator is in radical form.

34. anonymous

so how do i do that?

35. anonymous

Multiply both the numerator and denominator with the denominator.

36. anonymous

|dw:1438579262504:dw|

37. anonymous

Solve it, then that's the sine.

38. anonymous

39. anonymous

36

40. anonymous

sorry, I'm bad when it comes to anything with square roots

41. anonymous

So the numerator will be 36 sqrt 41.

42. anonymous

|dw:1438579466792:dw|

43. anonymous

ok.. now?

44. anonymous

For the denominator, just remove the radical sign, then multiply.

45. anonymous

so 9?

46. anonymous

No. Since we removed the radical sign, it will now be 3 times 41.

47. anonymous

ok so 123

48. anonymous

You forgot to multiply the other 3. :)

49. anonymous

this is so complicated lol

50. anonymous

|dw:1438579699524:dw|

51. anonymous

369

52. anonymous

Yes! :D

53. anonymous

Then simplify it. |dw:1438579781076:dw|

54. anonymous

55. anonymous

But we need to simplify it first.

56. anonymous

lol its never actually done

57. anonymous

HAHAHA one more step, then that's it; I promise. :D

58. anonymous

ok.

59. anonymous

Do you know how to simplify it?

60. anonymous

no

61. anonymous

:(

62. anonymous

Oh so we just need to find all of the factors of the numerator and denominator.

63. anonymous

Do you know the factor of 36? What do you multiply to get 36?

64. anonymous

2

65. anonymous

2 and ?

66. anonymous

18

67. anonymous

Great! So what are the numbers you'll multiply to get 18?

68. anonymous

Do you know the factor tree?

69. anonymous

i know how to simplify but not with the numerator being a square root

70. anonymous

Just ignore the square. :D

71. anonymous

So just simplify 36/369.

72. anonymous

okay

73. anonymous

74. anonymous

4/41

75. anonymous

sorry my laptop was at 1% and it wasn't charging so i was trying to fix that lol

76. anonymous

Good! So you just need to put back the sq rt of 41 to the numerator, then that's the sine.

77. anonymous

For cosine, just do what we did in the sine.

78. anonymous

so 4sqrt41/369?

79. anonymous

You already simplified it, why did you put back 369? :D

80. anonymous

i meant 41 I'm losing it lol

81. anonymous

i was looking back over everything lol

82. anonymous

Lol yes that's the sine.

83. anonymous

Now do the cosine.

84. anonymous

i think i got it from here. i can look back over it all.. thank you :)

85. anonymous

Sure! Once you did cosine, everything is now easy. Do you know how to get the tan now?

86. anonymous

What makes it harder is the rationalizing of the radicals, right? :D

87. anonymous

yes, thank you so much!

88. anonymous

you're welcome! if you need any help, just tag me.

89. anonymous

awesome! thanks!