anonymous
  • anonymous
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)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
is that t = 60 degrees?
amistre64
  • amistre64
so the point of 4,1 in the new system and it gives a choice of answers right?
anonymous
  • anonymous
Yes sorry Idk why it posted like that.

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amistre64
  • amistre64
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 ?
amistre64
  • amistre64
60-t is good -45.963 is your new angle... with a radius of sqrt(17) still right?
amistre64
  • amistre64
your new x and y are gonna be; x = sqrt(17) cos(-45.963) y = sqrt(17) sin(-45.963)
anonymous
  • anonymous
right... ok (2.866, -2.964)
anonymous
  • anonymous
so you found the angle of (4,1) subtracted that from the angle given. where did you get the 17 from?
amistre64
  • amistre64
the distance fromthe origin to the point is sqrt(4^2 + 1^2) = sqrt(17)
amistre64
  • amistre64
once you know the new angle; thats your radial measurement to convert it from polar to rects
anonymous
  • anonymous
oh ok I got it. Thanks!
amistre64
  • amistre64
60 is the sweep; minus the original angle = new angle formed by rotation of axis
amistre64
  • amistre64
sqrt(17) cos(new't'), sqrt(17) sin(new't') are your new coords right? :)
anonymous
  • anonymous
oakey dokey! so Yes they are! Cool thanks!
amistre64
  • amistre64
youre welcome :)

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