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Study23

Need help with these two vector problems! Given the following x and y components, find the magnitude and direction of the vector, counter clockwise from the x-axis: (1) x comp: -.5, y comp: 1. I found a magnitude of 1.12, but I'm having trouble with the angle. (2) x comp: -1.5 and y comp: -1; I got (1.80, 33.7 degrees, not sure if this is correct, though. I was confused with the negatives and to find the angle.

  • 6 months ago
  • 6 months ago

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  1. ganeshie8
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    mag = \(\sqrt{x^2+y^2}\) angle = \(\tan^{-1} \frac{y}{x}\)

    • 6 months ago
  2. Study23
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    I know, but I'm confused with the "counter clockwise from the x-axis" part of the problem.

    • 6 months ago
  3. ganeshie8
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    angle is always measured in counter clockwise, so dont wry about it

    • 6 months ago
  4. ganeshie8
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    |dw:1381000651274:dw|

    • 6 months ago
  5. ganeshie8
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    btw, ur magnitudes are correct, for angle just plug it in the formula

    • 6 months ago
  6. Study23
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    Is the angle for the second problem correct?

    • 6 months ago
  7. ganeshie8
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    nope

    • 6 months ago
  8. ganeshie8
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    clearly, that 2nd vector is in 4th quadrant, so we shud get angle >180

    • 6 months ago
  9. Study23
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    Hmmm, that's where I'm getting confused

    • 6 months ago
  10. ganeshie8
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    yeah :) just add 180 to that angle, as tan period is \(\pi\)

    • 6 months ago
  11. ganeshie8
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    |dw:1381001032077:dw|

    • 6 months ago
  12. Study23
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    Okay! I just realized as you said that I incorrectly drew the latter problem! The main problem I'm having is the angle for the first problem. When I set it up, (inverse tan) I got a negative angle????

    • 6 months ago
  13. ganeshie8
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    yeah, add 180 to that negative :) whats the big deal !

    • 6 months ago
  14. ganeshie8
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    sorry wait, negative angle is Clockwise, so from positive x direction, it wud be 360-\(\theta\)

    • 6 months ago
  15. ganeshie8
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    |dw:1381001359771:dw|

    • 6 months ago
  16. Study23
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    But how can it be in the 4th quadrant when -.5,1 is in 2nd quadrant?

    • 6 months ago
  17. Study23
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    wouldn't 360--thetha give me an angle over 360?

    • 6 months ago
  18. Study23
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    theta

    • 6 months ago
  19. ganeshie8
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    look at the figure, make out whats happening

    • 6 months ago
  20. ganeshie8
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    |dw:1381001694372:dw|

    • 6 months ago
  21. ganeshie8
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    the whole thing is 360 the vector is \(\theta\) fro positive x-axis clockwise direction

    • 6 months ago
  22. ganeshie8
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    so the vector wud be \(360-\theta\) from positive x-axis counter clockwise direction

    • 6 months ago
  23. Study23
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    Hmmm okay I guess that makes sense. Thank you!

    • 6 months ago
  24. ganeshie8
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    in \(-\theta\), minus just tells us the direction is clockwise

    • 6 months ago
  25. Study23
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    oh okay!!!!

    • 6 months ago
  26. ganeshie8
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    hey wat about this q of urs :- ``` But how can it be in the 4th quadrant when -.5,1 is in 2nd quadrant? ```

    • 6 months ago
  27. Study23
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    ?

    • 6 months ago
  28. ganeshie8
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    |dw:1381001958479:dw|

    • 6 months ago
  29. Study23
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    Yea, its in the 2nd quadrant

    • 6 months ago
  30. ganeshie8
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    angle = \(\large \tan^{-1}\frac{y}{x}\) \(\large \tan^{-1}\frac{-1}{.5}\) \(-63.43\) \(296.57\)

    • 6 months ago
  31. ganeshie8
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    add/subtract 180 to get to 2nd quadrant as tan period is \(\pi\)

    • 6 months ago
  32. Study23
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    So when do I use 180 v 360? Does the counter clock wise from +x affect that?

    • 6 months ago
  33. ganeshie8
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    when the angle is NEGATIVE, that means its measured in CLOCKWISE so subtract it from 360 to get COUNTER-CLOCKWISE

    • 6 months ago
  34. ganeshie8
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    |dw:1381002350796:dw|

    • 6 months ago
  35. Study23
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    And 180?

    • 6 months ago
  36. ganeshie8
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    180 comes from the fact that period of tan is 180 tan(x+180) = tan(x)

    • 6 months ago
  37. Study23
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    But when do you need to add 180?

    • 6 months ago
  38. ganeshie8
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    in this particular case, we clearly knw that the vector is in 2nd quadrant. but when we did the formula we got the angle in 4th quadrant, right ?

    • 6 months ago
  39. Study23
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    yes

    • 6 months ago
  40. ganeshie8
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    since adding/subtracting 180 to tan wont change its value, add/subtract 180 to get to 2nd quadrant

    • 6 months ago
  41. ganeshie8
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    |dw:1381002627185:dw|

    • 6 months ago
  42. ganeshie8
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    |dw:1381002685399:dw|

    • 6 months ago
  43. Study23
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    That makes sense!

    • 6 months ago
  44. Study23
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    Thank you so much for your help! I understand this now!

    • 6 months ago
  45. ganeshie8
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    np :)

    • 6 months ago
  46. Study23
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    :)

    • 6 months ago
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