1. Problem: Understand $360^\circ$ and its quadrants, and draw them in a circle. 2. Key idea (full turn): $360^\circ$ means one complete rotation. 3. Quadrants rule: A circle is split into $4$ equal parts. 4. Find the angle size of each quadrant: $$\frac{360^\circ}{4}=90^\circ$$ 5. Starting from the positive $x$-axis (right side) and moving counterclockwise: 1. Quadrant I: $0^\circ < \theta < 90^\circ$ 2. Quadrant II: $90^\circ < \theta < 180^\circ$ 3. Quadrant III: $180^\circ < \theta < 270^\circ$ 4. Quadrant IV: $270^\circ < \theta < 360^\circ$ 6. The boundary angles are where the rays land: - $0^\circ$ and $360^\circ$: positive $x$-axis - $90^\circ$: positive $y$-axis - $180^\circ$: negative $x$-axis - $270^\circ$: negative $y$-axis 7. Signs to remember: - Quadrant I: $(+,+)$ - Quadrant II: $(-,+)$ - Quadrant III: $(-,-)$ - Quadrant IV: $(+,-)$