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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.)

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  1. anonymous
    • one year ago
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    \[1'={\frac{1}{60}}^{\circ}\] \[180^{\circ}=\pi \space rad\]\[1^{\circ}=\frac{\pi}{180} \space rad\]\[{\frac{1}{60}}^{\circ}=?? \space rad\]

  2. anonymous
    • one year ago
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    What do you think?

  3. kittiwitti1
    • one year ago
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    I get 0.0002908...

  4. anonymous
    • one year ago
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    How much you are getting?

  5. anonymous
    • one year ago
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    Let me check

  6. kittiwitti1
    • one year ago
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    Okay.

  7. anonymous
    • one year ago
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    and what is the answer they've given?

  8. kittiwitti1
    • one year ago
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    Not mentioned.

  9. kittiwitti1
    • one year ago
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    I mean, it says "3 sig figs" and that would give me basically 0?

  10. anonymous
    • one year ago
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    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
    • one year ago
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    So... scientific notation?

  12. anonymous
    • one year ago
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    What exactly did you write for your answer?

  13. kittiwitti1
    • one year ago
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    I'd done it wrong before lol

  14. anonymous
    • one year ago
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    So your found your mistake?

  15. kittiwitti1
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    *puts in 0.000291* *gets right answer* WHAT.

  18. kittiwitti1
    • one year ago
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    THE HECK.

  19. anonymous
    • one year ago
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    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
    • one year ago
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    291. I had to round.

  21. kittiwitti1
    • one year ago
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    It's right.

  22. anonymous
    • one year ago
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    ahh, see

  23. kittiwitti1
    • one year ago
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    I'd put some entirely diff # before. lol

  24. anonymous
    • one year ago
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    anyways for your next part we have

  25. kittiwitti1
    • one year ago
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    2π+3π/4 didn't work

  26. anonymous
    • one year ago
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    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
    • one year ago
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    Did you get all that?

  28. anonymous
    • one year ago
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    Oh dear

  29. kittiwitti1
    • one year ago
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    10800??

  30. anonymous
    • one year ago
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    yep Here we have a=10800 \[{\frac{1}{60}}^{\circ}=\frac{\pi}{180} \times \frac{1}{60} \space rad\]

  31. kittiwitti1
    • one year ago
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    why is a 10800?

  32. anonymous
    • one year ago
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    ok first do you understand that \[1^{\circ}=\frac{\pi}{180} \space rad\]

  33. kittiwitti1
    • one year ago
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    Yes.

  34. anonymous
    • one year ago
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    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
    • one year ago
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    oh lol.

  36. kittiwitti1
    • one year ago
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    And yes.

  37. anonymous
    • one year ago
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    Now read my explanation above of how to convert it into terms of 2pi, i've written it above

  38. kittiwitti1
    • one year ago
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    I got lost.

  39. kittiwitti1
    • one year ago
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    o-o

  40. anonymous
    • one year ago
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    Ok i'll try again

  41. anonymous
    • one year ago
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    Suppose you have a fraction of the form \[\frac{\pi}{a}\]

  42. anonymous
    • one year ago
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    You can multiply it with 1, makes no difference, I'll write that just to create some clarity \[\frac{\pi(1)}{a}\]

  43. anonymous
    • one year ago
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    following so far?

  44. kittiwitti1
    • one year ago
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    Got it so far.

  45. anonymous
    • one year ago
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    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
    • one year ago
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    so far good?

  47. kittiwitti1
    • one year ago
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    Yep

  48. anonymous
    • one year ago
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    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
    • one year ago
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    So it makes no difference

  50. kittiwitti1
    • one year ago
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    Sorry; I'm tired so I take a while to process this stuff haha

  51. anonymous
    • one year ago
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    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
    • one year ago
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    Just keep responding if you are following, when you're not, let me know

  53. kittiwitti1
    • one year ago
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    Okay.

  54. kittiwitti1
    • one year ago
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    Actually... um, can you just tell me what's wrong with the equation I put in?

  55. anonymous
    • one year ago
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    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
    • one year ago
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    Sure, I'll see

  57. anonymous
    • one year ago
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    Where's your attempt ??

  58. kittiwitti1
    • one year ago
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    Eh ?

  59. anonymous
    • one year ago
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    You want me to check what you've done wrong for question 2, right?so let me see your work

  60. kittiwitti1
    • one year ago
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    http://icecream.me/3db4b88a7128b83b79b4db0bb933e6c5

  61. anonymous
    • one year ago
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    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
    • one year ago
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    You've expressed it in terms of pi not 2pi

  63. anonymous
    • one year ago
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    What number do you think when divided by 4 gives 2?

  64. kittiwitti1
    • one year ago
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    ?

  65. kittiwitti1
    • one year ago
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    \[\pi=\frac{4\pi}{4}?\rightarrow \pi+\frac{3\pi}{4}=\frac{4\pi}{4}+\frac{3\pi}{4}=\frac{7\pi}{4}\]

  66. anonymous
    • one year ago
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    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
    • one year ago
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    I want to express it in terms of pi?

  68. anonymous
    • one year ago
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    Nope, check your question

  69. kittiwitti1
    • one year ago
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    ! FFFFFF

  70. kittiwitti1
    • one year ago
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    So then:\[2\pi-\frac{\pi}{4}\]

  71. anonymous
    • one year ago
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    yep!

  72. kittiwitti1
    • one year ago
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    BAH I feel dumb

  73. kittiwitti1
    • one year ago
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    What about part 3?

  74. anonymous
    • one year ago
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    You didn't post any part 3

  75. anonymous
    • one year ago
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    oh I see it now

  76. kittiwitti1
    • one year ago
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    You sure? :p

  77. kittiwitti1
    • one year ago
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    xD

  78. anonymous
    • one year ago
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    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
    • one year ago
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    Whut.

  80. kittiwitti1
    • one year ago
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    Gimme a sec lol

  81. anonymous
    • one year ago
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    We are given 1 minute in the question, not 1 degree

  82. kittiwitti1
    • one year ago
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    Okay I got what you said.

  83. kittiwitti1
    • one year ago
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    But I'm not sure where to go from here.

  84. anonymous
    • one year ago
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    well just calculate the product and you'd get the relation between a nautical mile and miles

  85. kittiwitti1
    • one year ago
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    okay

  86. kittiwitti1
    • one year ago
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    1.164 is what I got

  87. anonymous
    • one year ago
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    Should be it

  88. kittiwitti1
    • one year ago
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    Alright

  89. kittiwitti1
    • one year ago
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    Thanks! :D

  90. kittiwitti1
    • one year ago
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    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
    • one year ago
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    nvm I got it right now

  92. anonymous
    • one year ago
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    Extremely sorry I didn't notice, I was studying myself, but I'm glad you got it anyway.

  93. kittiwitti1
    • one year ago
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    xD

  94. kittiwitti1
    • one year ago
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    S'alright. I think I'm good now, you don't have to stay :]

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