New_X = Old_X * Cos ( angle )

Solved

Posted on 2006-04-24

Hi experts,

I'm looking for some help with trigonometry, more specifically rotating 4 points around a centre point.

I have a rectangle, with centre point 0,0 and want to rotate this counter-clockwise a variable number of degrees. Say 45 degrees for example. The 4 points on the rectangle are 6,3 : -6,3 : -6,-3 : 6,3.

I know this involves sin and cos but I cannot figure out how to use these functions.

So, simply put - how do i work out the new coordinates for a rotation of 45 degrees for the above coordinates.

Any help would be appreciated.

Thanks in advance,

Eoin.

I'm looking for some help with trigonometry, more specifically rotating 4 points around a centre point.

I have a rectangle, with centre point 0,0 and want to rotate this counter-clockwise a variable number of degrees. Say 45 degrees for example. The 4 points on the rectangle are 6,3 : -6,3 : -6,-3 : 6,3.

I know this involves sin and cos but I cannot figure out how to use these functions.

So, simply put - how do i work out the new coordinates for a rotation of 45 degrees for the above coordinates.

Any help would be appreciated.

Thanks in advance,

Eoin.

10 Comments

( 6*Cos(45), 3*Sin(45) ) =~ ( 4.2, 2.12 )

New_Y = Old_Y * cos( angle ) + old_x * sin(angle)

New_X = Old_X * Cos ( angle ) - old_y*sin(angle)

Notice that when angle=0, the cos is 1 and the sin is 0, so new_x = old_x and new_y = old_y

Radius, from 0,0 to 6,3, using pythagoras' = 6.7

sqrt(6^2 + 3^2)

sqrt(45) = ~6.7

new_X = radius * cos (angle)

new_X = 6.7 * cos(45)

new_X = 2.1

new_Y = radius * sin (angle)

new_Y = 6.7 * sin(45)

new_Y = 6.4

so 6, 3 rotates to 2.1, 6.4 ?

Is this correct?

The other numbers are confusing me because of all this quadrant and negative number stuff, anyone have any ideas?

Thanks again,

Eoin

First i got the previous angle using Tan (angle) = Opposite / Adjacent

Tan (angle) = 3/6

Tan (angle) = 0.5

Angle = ~27 degrees

So new angle to work with is 27+45 = 72 degrees

I then used

radius * cos (new angle)

radius * sin (new angle)

Does this make sense? It looks correct on a poorly drawn excel spreadsheet i made :)

New_Y = Old_Y * cos + old_x * sin

New_X = Old_X * Cos - old_y*sin

new_x^2 + new_y^2 = (old_y*cos + old_x*sin)^2 + (old_x*cos - old_y*sin)^2

= old_y^2 * cos^2 + 2*old_x*old_y*cos*sin + old_x^2*sin^2 + old_x^2*cos^2 - 2*old_x*old_y*cos*sin + old_y^2*sin^2

= old_y^2*(cos^2 + sin^2) + (2 - 2)*(old_x*old_y*cos_sin) + old_x*(cos^2 + sin^2)

new_x^2 + new_y^2 = old_y^2 + old_x^2

eg.

if the point is 2.5, 30 degrees after rotating by 45 degrees the point is now 2.5, 75 degrees.

I used your expression for the top right point (6,3) and it worked. However when I try the same expression for negative numbers the results are off.

I read a bit about quadrants and that they change positives and negatives depending on which one you are working in. Can anyone elaborate?

AndyAinscow,

Thanks for your input, however I don't think polar co-ordinates will be beneficial as I have a cartesian map to work with - it might be one unneccessary complication too many ;)

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