Parameters
Starting Angle (θ)
0.785 radRadius (r)r = 1
Fixed at unit circle
Rotation Angle (α)
0.000 radRotation in 2D
t: 0.00s
Rotation Matrix
[
=x′y′
][
cos αsin α-sin αcos α
][
xy
][
=x′y′
][]
xcos α + ysin α
ycos α - xsin α
Original: x = 0.707, y = 0.707
Rotated: x′ = 0.707, y′ = 0.707
cos(α) = 1.000, sin(α) = 0.000
Point vs Axes Rotation
Key insight: Rotating a point by +α is equivalent to rotating the axes by -α. The component magnitudes (colored lines) are identical in both views.