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)

Question

amistre64 · Answer

is that t = 60 degrees?

amistre64 · Answer

so the point of 4,1 in the new system and it gives a choice of answers right?

anonymous · Answer

Yes sorry Idk why it posted like that.

amistre64 · Answer

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 · Answer

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

amistre64 · Answer

your new x and y are gonna be;

x = sqrt(17) cos(-45.963)

y = sqrt(17) sin(-45.963)

anonymous · Answer

right... ok (2.866, -2.964)

anonymous · Answer

so you found the angle of (4,1) subtracted that from the angle given. where did you get the 17 from?

amistre64 · Answer

the distance fromthe origin to the point is sqrt(4^2 + 1^2) = sqrt(17)

amistre64 · Answer

once you know the new angle; thats your radial measurement to convert it from polar to rects

anonymous · Answer

oh ok I got it. Thanks!

amistre64 · Answer

60 is the sweep; minus the original angle = new angle formed by rotation of axis

amistre64 · Answer

sqrt(17) cos(new't'), sqrt(17) sin(new't') are your new coords right?  :)

anonymous · Answer

oakey dokey! so Yes they are! Cool thanks!

amistre64 · Answer

youre welcome :)