Problem: A point starts at (1, 0) on the unit circle and rotates 90° counterclockwise about the origin. Where does it end up?
Step 1: Counterclockwise rotation on a standard coordinate plane moves from the positive x-axis toward the positive y-axis.
Step 2: A 90° counterclockwise rotation sends the point (x, y) to (-y, x).
(−y,x)=(−(0),1)=(0,1)
Answer: The point moves from (1, 0) to (0, 1), landing on the top of the unit circle.
Why It Matters
Counterclockwise is the standard positive direction of rotation in mathematics. When you see a positive angle like 45° or 3π radians, the rotation is assumed to be counterclockwise unless stated otherwise. This convention is used throughout trigonometry, physics, and engineering whenever angles or rotations are measured.
Common Mistakes
Mistake: Confusing the sign of a rotation angle — assuming a positive angle means clockwise.
Correction: By mathematical convention, positive angles correspond to counterclockwise rotation, while negative angles correspond to clockwise rotation.
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