what is the measurement of (2,2) if rotated 305 degrees

1 answer

To find the new coordinates after rotating a point (2,2) by 305 degrees, we can use the rotation matrix formula.

The rotation matrix for counterclockwise rotation by an angle θ is given by:
[ cos(θ) -sin(θ) ]
[ sin(θ) cos(θ) ]

In this case, θ = 305 degrees. Converting 305 degrees to radians, we get:
θ = 305 * π/180 = 5.327 radians

Using the rotation matrix, we can find the new coordinates by multiplying the rotation matrix with the given point coordinates (2,2):

[ cos(5.327) -sin(5.327) ] [ 2 ]
[ sin(5.327) cos(5.327) ] * [ 2 ]

Calculating the matrix multiplication gives:
[ 1.891 -1.069 ]
[ 1.069 1.891 ]

Therefore, the rotated coordinates are approximately (1.891, 1.069)