## kittiwitti1 one year ago SUBJECT TO EDITING. Trig questions: #1: Use 3.1416 for π unless your calculator has a key marked π. Use a calculator to convert 1' (1 minute) to radians to three significant digits. #2: Write the angle as a difference involving 2π. For example, 5π/3 = 2π − π/3. 7π/4 #3: If a central angle with its vertex at the center of the earth has a measure of 1', then the arc on the surface of the earth that is cut off by this angle (known as the great circle distance) has a measure of 1 nautical mile (see the figure below). Find the number of regular (statute) miles in 1 nautical mile to the nearest hundredth of a mile. (Use 4,000 miles for the radius of the earth.)

1. anonymous

$1'={\frac{1}{60}}^{\circ}$ $180^{\circ}=\pi \space rad$$1^{\circ}=\frac{\pi}{180} \space rad$${\frac{1}{60}}^{\circ}=?? \space rad$

2. anonymous

What do you think?

3. kittiwitti1

I get 0.0002908...

4. anonymous

How much you are getting?

5. anonymous

Let me check

6. kittiwitti1

Okay.

7. anonymous

and what is the answer they've given?

8. kittiwitti1

Not mentioned.

9. kittiwitti1

I mean, it says "3 sig figs" and that would give me basically 0?

10. anonymous

Your answer is absolutely correct, you can eve google "minutes to radian conversion" I think zeros after a decimal don't count as significant unless they are after some other number, I might be remembering that wrong though

11. kittiwitti1

So... scientific notation?

12. anonymous

13. kittiwitti1

I'd done it wrong before lol

14. anonymous

15. kittiwitti1

No... I'm not sure if this is the right answer, so I'd have to check and make sure. I'm not sure how many attempts I have left x_x

16. anonymous

Oh, if you are giving an online test/exam, they sometimes require you to write in a particular way, but mathematically your answer is 100% correct

17. kittiwitti1

*puts in 0.000291* *gets right answer* WHAT.

18. kittiwitti1

THE HECK.

19. anonymous

I see your mistake now, why are you writing 2.91?? Write the answer that we found! 0.000290 - upto 3 significant figures!

20. kittiwitti1

21. kittiwitti1

It's right.

22. anonymous

ahh, see

23. kittiwitti1

I'd put some entirely diff # before. lol

24. anonymous

anyways for your next part we have

25. kittiwitti1

2π+3π/4 didn't work

26. anonymous

You want to express the following fraction in terms of 2pi $\frac{\pi}{10800}$ So if you were to somehow split the numerator to express it as a sum of 2 fractions, you'd want 1 of the fractions to have a numerator of 2 times the denominator so that you get 2pi upon cancelling $\frac{\pi}{a}=\frac{\pi(1)}{a}=\frac{\pi(1+b-b)}{a}=\frac{b \pi+(1-b)\pi}{a}=\frac{b \pi}{a}+\frac{(1-b)\pi}{a}$ b is any arbitrary constant, we will choose b such that $b=2a$ So substituting we get $\frac{2a \pi}{a}+\frac{(1-2a)\pi}{a}=2\pi+\frac{(1-2a)\pi}{a}$ Here we have $a=10800$

27. anonymous

Did you get all that?

28. anonymous

Oh dear

29. kittiwitti1

10800??

30. anonymous

yep Here we have a=10800 ${\frac{1}{60}}^{\circ}=\frac{\pi}{180} \times \frac{1}{60} \space rad$

31. kittiwitti1

why is a 10800?

32. anonymous

ok first do you understand that $1^{\circ}=\frac{\pi}{180} \space rad$

33. kittiwitti1

Yes.

34. anonymous

So now we want to find $1'={\frac{1}{60}}^{\circ}$ How would you do that?you'd divide by 60 of course! Don't worry, I said that oh dear because you were lagging and I was afraid you may have to leave the question in between

35. kittiwitti1

oh lol.

36. kittiwitti1

And yes.

37. anonymous

Now read my explanation above of how to convert it into terms of 2pi, i've written it above

38. kittiwitti1

I got lost.

39. kittiwitti1

o-o

40. anonymous

Ok i'll try again

41. anonymous

Suppose you have a fraction of the form $\frac{\pi}{a}$

42. anonymous

You can multiply it with 1, makes no difference, I'll write that just to create some clarity $\frac{\pi(1)}{a}$

43. anonymous

following so far?

44. kittiwitti1

Got it so far.

45. anonymous

Now, we can add and subtract any number, it will make no difference Suppose we have some equation $x^2+2x+3=9$ If we add and subtract say, root 7, it will make no difference to the equation overall $x^2+2x+3+\sqrt{7}-\sqrt{7}=9$ Similarly we add and subtract an arbitrary constant b $\frac{\pi(1+b-b)}{a}$ We can take b as whatever we want, but there's a particular value of b we desire, I'll show you what value later

46. anonymous

so far good?

47. kittiwitti1

Yep

48. anonymous

To further illustrate, I'll distribute the pi and see what we get $\frac{\pi(1+b-b)}{a}=\frac{\pi+b \pi-b \pi}{a}=\frac{\pi}{a}$

49. anonymous

So it makes no difference

50. kittiwitti1

Sorry; I'm tired so I take a while to process this stuff haha

51. anonymous

Next we will split our fraction into 2 fractions $\frac{\pi(b+1-b)}{a}=\frac{\pi b+\pi(1-b)}{a}=\frac{\pi b}{a}+\frac{\pi(1-b)}{a}$

52. anonymous

Just keep responding if you are following, when you're not, let me know

53. kittiwitti1

Okay.

54. kittiwitti1

Actually... um, can you just tell me what's wrong with the equation I put in?

55. anonymous

Now b can take value we want, right? This is because we can add AND subtract any number from an equation or an expression at the same time So if we were to let $b=2a$ That is completely valid and allowed, like I said b can take any value

56. anonymous

Sure, I'll see

57. anonymous

58. kittiwitti1

Eh ?

59. anonymous

You want me to check what you've done wrong for question 2, right?so let me see your work

60. kittiwitti1
61. anonymous

Oh I see, so they want you to express $\frac{7\pi}{4}$ I thought they meant the answer you got from 1st part

62. anonymous

You've expressed it in terms of pi not 2pi

63. anonymous

What number do you think when divided by 4 gives 2?

64. kittiwitti1

?

65. kittiwitti1

$\pi=\frac{4\pi}{4}?\rightarrow \pi+\frac{3\pi}{4}=\frac{4\pi}{4}+\frac{3\pi}{4}=\frac{7\pi}{4}$

66. anonymous

You want to express it in terms of 2pi you are expressing in terms of pi Answer me and you'll solve it, what number when divided by 4 will give u 2?

67. kittiwitti1

I want to express it in terms of pi?

68. anonymous

69. kittiwitti1

! FFFFFF

70. kittiwitti1

So then:$2\pi-\frac{\pi}{4}$

71. anonymous

yep!

72. kittiwitti1

BAH I feel dumb

73. kittiwitti1

74. anonymous

You didn't post any part 3

75. anonymous

oh I see it now

76. kittiwitti1

You sure? :p

77. kittiwitti1

xD

78. anonymous

ok so first we have $r=4000 \space mile$$l=1 \space nautical \space mile$$\theta=1'=\frac{\pi}{10800} \space rad$ We have the formula |dw:1444468327841:dw| $l=r \theta$ Where, theta is in radians, very important! so we get $1 \space nautical \space mile = 4000 \times \frac{\pi}{10800} \space miles$ We already calculated the value of the angle earlier in radians it was about $\theta \approx 0.000291$$1 \space nautical \space mile = 4000 \times 0.000291 \space miles$

79. kittiwitti1

Whut.

80. kittiwitti1

Gimme a sec lol

81. anonymous

We are given 1 minute in the question, not 1 degree

82. kittiwitti1

Okay I got what you said.

83. kittiwitti1

But I'm not sure where to go from here.

84. anonymous

well just calculate the product and you'd get the relation between a nautical mile and miles

85. kittiwitti1

okay

86. kittiwitti1

1.164 is what I got

87. anonymous

Should be it

88. kittiwitti1

Alright

89. kittiwitti1

Thanks! :D

90. kittiwitti1

Oh, another question @Nishant_Garg Evaluate the following expression when x is π/6. Use exact values. 4 cos(2x + π/3 ) I put the below link and was told it was incorrect: http://icecream.me/740b0853764307a397859eaad1391961

91. kittiwitti1

nvm I got it right now

92. anonymous

Extremely sorry I didn't notice, I was studying myself, but I'm glad you got it anyway.

93. kittiwitti1

xD

94. kittiwitti1

S'alright. I think I'm good now, you don't have to stay :]