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anonymous

  • 5 years ago

The x'y'-coordinate system has been rotated θ degrees from the xy-coordinate system. The coordinates of a point in the xy-coordinate system are given. Find the coordinates of the point in the rotated system. Round to three decimal places, if necessary. θ=60°, (4,1) A. (- 2.964, 2.866) B. (2.866, - 2.964) C. (- 2.866, 2.964) D. (2.964, - 2.866) E. (1.134, 3.964)

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  1. amistre64
    • 5 years ago
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    is that t = 60 degrees?

  2. amistre64
    • 5 years ago
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    so the point of 4,1 in the new system and it gives a choice of answers right?

  3. anonymous
    • 5 years ago
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    Yes sorry Idk why it posted like that.

  4. amistre64
    • 5 years ago
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    the angle of (4,1) = tan^-1(1/4) = 14.036 degrees to begin with right? now sweep 60 past that and you should be what 60 - t ?

  5. amistre64
    • 5 years ago
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    60-t is good -45.963 is your new angle... with a radius of sqrt(17) still right?

  6. amistre64
    • 5 years ago
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    your new x and y are gonna be; x = sqrt(17) cos(-45.963) y = sqrt(17) sin(-45.963)

  7. anonymous
    • 5 years ago
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    right... ok (2.866, -2.964)

  8. anonymous
    • 5 years ago
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    so you found the angle of (4,1) subtracted that from the angle given. where did you get the 17 from?

  9. amistre64
    • 5 years ago
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    the distance fromthe origin to the point is sqrt(4^2 + 1^2) = sqrt(17)

  10. amistre64
    • 5 years ago
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    once you know the new angle; thats your radial measurement to convert it from polar to rects

  11. anonymous
    • 5 years ago
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    oh ok I got it. Thanks!

  12. amistre64
    • 5 years ago
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    60 is the sweep; minus the original angle = new angle formed by rotation of axis

  13. amistre64
    • 5 years ago
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    sqrt(17) cos(new't'), sqrt(17) sin(new't') are your new coords right? :)

  14. anonymous
    • 5 years ago
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    oakey dokey! so Yes they are! Cool thanks!

  15. amistre64
    • 5 years ago
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    youre welcome :)

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