A Ferris wheel is drawn on a coordinate plane so that the first car is located at the point (40,0). What are the coordinates of the first car after a rotation of 270 degrees counterclockwise about the origin?
Steve is a no help sceezer
To Amber: Agreed. I came here looking for cheats, not actual work
To find the coordinates of the first car after a rotation of 270 degrees counterclockwise about the origin, we can use the rotation matrix. The rotation matrix for a counterclockwise rotation of angle θ about the origin is:
[ cos(θ) -sin(θ) ]
[ sin(θ) cos(θ) ]
In this case, θ is 270 degrees. So, substituting the values, we get:
[ cos(270°) -sin(270°) ]
[ sin(270°) cos(270°) ]
Now, let's calculate the cosine and sine of 270 degrees:
cos(270°) = 0
sin(270°) = -1
Now, substitute these values into the rotation matrix:
[ 0 -(-1) ]
[ -1 0 ]
Simplifying, we get the rotation matrix:
[ 0 1 ]
[ -1 0 ]
To find the new coordinates of the point (40,0) after rotation, we multiply the rotation matrix by the original point:
[ 0 1 ] [ 40 ]
[ -1 0 ] * [ 0 ]
Performing the matrix multiplication, we get:
[ 1*40 + 0*0 ]
[ 0*40 + (-1)*0 ]
Simplifying further:
[ 40 ]
[ 0 ]
Therefore, the new coordinates of the first car after a rotation of 270 degrees counterclockwise about the origin are (40, 0).