anonymous one year ago Explain SOH-CAH-TOA sin=______ cos=______ tan=_______

1. anonymous

@peachpi

2. triciaal

|dw:1440640439967:dw|

3. triciaal

|dw:1440640548365:dw|

4. anonymous

O thanks :)

5. triciaal

SOH -CAH-TOA is a "code" used to remember the trig identities this is with a right triangle the hypotenuse is always opposite the right angle and is the longest side of the triangle

6. anonymous

If i wanted to know sin cos and tan but in terms of not using opp hyp and adj. what would they look like?

7. anonymous

@triciaal

8. anonymous

they would be points on the unit circle where the input was the angle, and the output for cosine is the first coordinate and for sine the second coordinate of that point

9. anonymous

10. anonymous

i kind of dont understand

11. anonymous

@satellite73

12. anonymous

if you are using the mnemonic device soh cah toa , save what i sent for later it will be a big help believe me, but you are not ready for it yet

13. anonymous

ok

14. anonymous

i just dont know what to put in the blanks in number 5

15. anonymous

oh i think they want you to say$\sin(\theta)=\frac{y}{r},\cos(\theta)=\frac{x}{r},\tan(\theta)=\frac{y}{x}$

16. anonymous

whoever wrote this made a very serious error however

17. anonymous

what was the error? It was my teacher btw lol

18. anonymous

sine is a function, it is spelled "sine" if you want to write it in function notation, it needs to be $$\sin(\theta)$$ or $$\sin(\xi)$$ or $$\sin(\clubsuit)$$ or something with a variable in the parentheses not "sin = " which makes no sense at all

19. anonymous

you can tell him/her satellite said they were abusing notation which will lead to massive confusion for you down the road

20. anonymous

Oh, ill be sure to tell her. What would i label the side lying on the x axix and the vertical side??

21. anonymous

x and y i guess

22. anonymous

|dw:1440642321127:dw|

23. anonymous

|dw:1440642400091:dw|

24. anonymous

|dw:1440642460037:dw|

25. anonymous

is that it?

26. anonymous

yeah looks good

27. anonymous

btw in the picture you have a $$\theta$$ as the angle, so it should be $$\sin(\theta)$$ etc also note that $$r=\sqrt{x^2+y^2}$$ by pythagoras

28. anonymous

all right. Thanks. can you guide me with this?

29. triciaal

#6 use pythagoren theorem @satellite73 has it above

30. anonymous

yeah we just anticipated that question when i said $r=\sqrt{x^2+y^2}$ so if, for example the point was $$(2,5)$$ you would have $r=\sqrt{2^2+5^2}$

31. anonymous

i notice on this page at least, the $$\theta$$'s have made an appearance !

32. anonymous

Lol. Would i leave it |dw:1440642870108:dw|

33. anonymous

34. anonymous

ok

35. anonymous

notice it says "no decimal"

36. anonymous

yeah. i just seen that

37. anonymous

So #7 would be |dw:1440643014145:dw|

38. anonymous

nvm

39. anonymous

lol

40. anonymous

|dw:1440643104712:dw|

41. anonymous

it is really $\sin(\theta)=\frac{5}{\sqrt{29}}$ but that is not what they want as a "final answer"q

42. anonymous

yeah cause i cant leave the 29 like that.

43. anonymous

I would have to multiply ???

44. anonymous

aka "rationalize the denominator "

45. anonymous

$\frac{5}{\sqrt{29}}\times \frac{\sqrt{29}}{\sqrt{29}}=\frac{5\sqrt{29}}{29}$ with a tiny bit of practice you do this in your head

46. anonymous

|dw:1440643207188:dw|

47. anonymous

there should be a 29 in the denominator

48. anonymous

So thats r??

49. anonymous

no $$r=\sqrt{29}$$

50. anonymous

$\sin(\theta)=\frac{5\sqrt{29}}{29}$

51. anonymous

hmmm so cos (theta)= 2/29?

52. anonymous

no $\cos(\theta)=\frac{2}{\sqrt{29}}=\frac{2\sqrt{29}}{29}$

53. anonymous

Tan = 5/2??

54. anonymous

yes

55. anonymous

nice. im doing #8 now

56. anonymous

ok find r as before, then use the same ratios as before

57. anonymous

ok

58. anonymous

the negatives are messing me up when im using the ratios

59. anonymous

Am i suppose to us positives??

60. anonymous

no

61. triciaal

plot the points and pay attention to the signs

62. anonymous

leave them as negative

63. anonymous

the tangent will be positive since you have two negatives, but the sine and cosine are negative for sure

64. triciaal

|dw:1440644210522:dw|

65. anonymous

So is this correct????

66. triciaal

|dw:1440644481593:dw|

67. triciaal

correct

68. anonymous

I got it correct??

69. triciaal

now you have the CAST rule

70. triciaal

|dw:1440644731475:dw|

71. triciaal

another mnemonic to remember what ratios are positive in which quadrant

72. anonymous

ok thanks

73. triciaal

A for all positive in quadrant 1

74. triciaal

you are welcome

75. anonymous

@satellite73

76. anonymous

@triciaal What about the S T C

77. anonymous

78. anonymous

@satellite73