Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ilikephysics2

HELP Find the area of the region that lies inside both curves r = 8sin(2theta), r = 8sin(theta)

  • one year ago
  • one year ago

  • This Question is Closed
  1. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    let me guess, third year calculus?

    • one year ago
  2. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah why?

    • one year ago
  3. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    It was torture for me :) let me see if I can help, I need some scratch paper though

    • one year ago
  4. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    ok thanks man its so tough

    • one year ago
  5. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    i can relate, gimmie a sec

    • one year ago
  6. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

    • one year ago
  7. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    have you done double integrals?

    • one year ago
  8. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    Not yet

    • one year ago
  9. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    dang, okay gotta think of how to do this using single...

    • one year ago
  10. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    we haven't gotten that far we are in chapter 9 with areas of regions and in curves

    • one year ago
  11. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    give me as much info as you can then

    • one year ago
  12. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    well the question is just right there lol, idk what else you want

    • one year ago
  13. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    we have done polar coordinates, taylor series , maclaurin series

    • one year ago
  14. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    okay good, you can't do this in rectangular, polar is your best, no only shot unless you want roots. it's also cleaner. I just need to remember how to do a single integral sadly. I haven't done Calc 3 in a long time

    • one year ago
  15. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah I hear you, I'm looking at this problem and I don't even know where to start, if you can show me step by step what you do, that would be so helpful

    • one year ago
  16. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    \[8\sin(2\theta)=8\sin(\theta)\] \[\sin(2\theta)=\sin(\theta)\] \[2\sin(\theta)\cos(\theta)=\sin(\theta)\] \[2\sin(\theta)\cos(\theta)-\sin(\theta)=0\] \[\sin(\theta)(2\cos(\theta)-1)=0\] \[\sin(\theta)=0\] and \[2\cos(\theta)-1=0\] Solve for theta and these are your limits of integration.

    • one year ago
  17. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    Notice how I cancelled the 8 but didn't cancel the sin(theta). You never want to cancel out anything that isn't a constant since it might be a potential solution.

    • one year ago
  18. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    ok I see

    • one year ago
  19. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    Can you pick it up from there since you've done polar coordinates? I don't know if you've done integration using polar yet or not.

    • one year ago
  20. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    so its 2 cos(theta) = 1, so cos(theta) = 1/2?

    • one year ago
  21. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    But believe me, you'll need a strong grip on polar since double and triple integrals build on that. Cylindrical is like a second layer to polar and spherical...well just be strong in polar and double and triple will be easier for you

    • one year ago
  22. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes

    • one year ago
  23. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    OK so i have sin(theta) = 0 and cos(theta) = 1/2

    • one year ago
  24. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    yep, and notice how both functions are even( you're in polar not rectangular) so you need to take into account the negative answer

    • one year ago
  25. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok so now what?

    • one year ago
  26. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    what are your values for theta?

    • one year ago
  27. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    0 and 1/2?

    • one year ago
  28. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    come on, your values for theta, not sin(theta) and cos(theta). Think trig or geometry. This is calculus so if you're willing to take calc, especially calc 3, you should know how to take the inverse of a trig function.

    • one year ago
  29. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    I thought you meant those values though

    • one year ago
  30. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    theta refers to the angle. What are the angles? Stop and don't think calculus right now. Go back to your geometry or trig. How did you find an angle using trig functions like sine and cosine?

    • one year ago
  31. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    The circle, so wouldn't it be 30 degrees

    • one year ago
  32. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1351461552476:dw|

    • one year ago
  33. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    I barely remember the unit circle

    • one year ago
  34. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    That is a right triangle. Forget the unit circle, focus on the triangle. Cosine of which angle will give you 1/2? What two sides do you use for cosine? |dw:1351461655567:dw|

    • one year ago
  35. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    I thought it was 30 degrees?

    • one year ago
  36. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh and use that graph for sine. It's crappy but it was the best I had. Ok, what is cosine? Think back to your geometry.

    • one year ago
  37. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    sqrt(3)/2?

    • one year ago
  38. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    That is the best I could remember

    • one year ago
  39. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    no, no, the DEFINITION of cosine

    • one year ago
  40. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    like which degree or just the definition?

    • one year ago
  41. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    forget all numbers

    • one year ago
  42. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    A/H

    • one year ago
  43. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    forget angles, forget numbers, just the textbook definition

    • one year ago
  44. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    GOOD.

    • one year ago
  45. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    Okay, so what is A/H?

    • one year ago
  46. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    what does it stand for?

    • one year ago
  47. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    sqrt(3)/2

    • one year ago
  48. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    adjacent over hypotenuse

    • one year ago
  49. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    good, now when we had \[2\cos(\theta)-1=0\] how did you solve it?

    • one year ago
  50. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    I got cos(theta) = 1/2 by adding then dividing

    • one year ago
  51. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    good, now look at that triangle I drew. Do you see a 1 for the adjacent, and 2 for the hypotenuse?

    • one year ago
  52. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh yeah so 1/2

    • one year ago
  53. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    right, when you have a fraction, that's what that fraction means

    • one year ago
  54. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

    • one year ago
  55. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    so what angle, 30, 60, or 90, will give you cos(theta)=1/2?

    • one year ago
  56. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    Nope 60 degrees since its a/h which is 1/2

    • one year ago
  57. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1351462522741:dw|

    • one year ago
  58. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    60 degrees will give us 1/2

    • one year ago
  59. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    got it! so theta is 60 degrees or pi/3

    • one year ago
  60. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    ok yes cause they are equivalent

    • one year ago
  61. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, so can you do the same for\[\sin(\theta)=0\]

    • one year ago
  62. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    Hint: you can't do this using a triangle

    • one year ago
  63. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    its just 0

    • one year ago
  64. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    bingo

    • one year ago
  65. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    those are your limits of integration

    • one year ago
  66. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    so 0 to pi/3?

    • one year ago
  67. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, but do you remember the area(not under a curve) between two curves?

    • one year ago
  68. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    how would you integrate if I said y=x^2 and y=3-4x^2?

    • one year ago
  69. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    like Big R ^2 - Little r ^2?

    • one year ago
  70. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    YES

    • one year ago
  71. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    so we have 0 to pi/3 of our 2 functions?

    • one year ago
  72. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    now you have your limits of integration (in radians). You need to figure out which is the top function and which is the bottom

    • one year ago
  73. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    top is 8 sin(theta) and bottom is 8sin(2theta)

    • one year ago
  74. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    Did you guess that?

    • one year ago
  75. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    No I graphed it

    • one year ago
  76. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    Ok, so then you know we're missing the left part of the graph then correct? since we are only going from 0 to pi/3

    • one year ago
  77. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    so then we have to go from -pi/3 to 0?

    • one year ago
  78. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    Nope, don't go into negative. Use the trace on your calculator and you'll see that the graph keeps going from 0 to 2pi. A lot of graphs are like that but not all

    • one year ago
  79. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    so whats our final integral going to look like then?

    • one year ago
  80. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    Remember, the independent variable here isn't x like in rectangular coordinates, the angle theta (in radians) is the independent variable. Both x and y are dependent

    • one year ago
  81. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    Good question. There are actually two limits I didn't want to get into yet, but since you brought it up, there are TWO solutions to both sin(theta)=0 and cos(theta)=1/2 (within the restriction that theta is from 0 to 2pi.) Without that restriction, theta would have an infinite number of solutions

    • one year ago
  82. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    You realize this is not a double intgreal question right?

    • one year ago
  83. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    yup, you're going to add the two integrals, just like if you had a break in the middle of a graph

    • one year ago
  84. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    So integral from 0 to 2pi (8sin(theta)-8sin(2theta)) + 0 to pi/3 ((8sin(theta)-8sin(2theta))

    • one year ago
  85. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1351463619332:dw|

    • one year ago
  86. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    notice how if you did top minus bottom( which is the x axis) you need to change your limits of integration?

    • one year ago
  87. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    It's the same idea here, but using polar

    • one year ago
  88. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    it is top-bottom though

    • one year ago
  89. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    Can you draw out what the ending integral will look like

    • one year ago
  90. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    true, you're right there, just that the limits(BOTH LIMITS) will change

    • one year ago
  91. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1351463857221:dw|

    • one year ago
  92. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah I have that

    • one year ago
  93. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    I focused on three points, but one of those points is actually a different limit of integration. For the graph of sine, what TWO values will give you 0? That's a big hint on your limits.

    • one year ago
  94. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok cool thanks I think I got it from here

    • one year ago
  95. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    I hope I didn't hold back too much, but I wanted you to think and not just give you the answers. I hope I did okay

    • one year ago
  96. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    it was good thanks, I still have to solve for the answer though, what was your result? Mine was 12.75516082

    • one year ago
  97. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    uh...do you by any chance have the answer? Just a yes or no.

    • one year ago
  98. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    Back of the book I mean

    • one year ago
  99. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    yes thats my answer, oh no its webwork

    • one year ago
  100. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    webwork didnt take my answer

    • one year ago
  101. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    Uh, I got an 8...

    • one year ago
  102. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    and no idea what webwork is

    • one year ago
  103. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    what did you get 8 what?

    • one year ago
  104. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    8 as the final answer

    • one year ago
  105. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    Is that the answer in your text?

    • one year ago
  106. ilikephysics2
    Best Response
    You've already chosen the best response.
    Medals 0

    ok but our answers are both wrong

    • one year ago
  107. roadjester
    Best Response
    You've already chosen the best response.
    Medals 1

    OUGH

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.