1. For angle 5π/4:
- Start from the positive x-axis (standard position).
- Since 5π/4 = π + π/4, rotate counterclockwise past π (180°) by an additional π/4 (45°).
- The terminal side lies in Quadrant III, exactly halfway between the negative x-axis and negative y-axis.
2. For angle -47π/18:
- First, simplify the angle by adding multiples of 2π to get a coterminal angle between 0 and 2π.
- -47π/18 + 3×2π = -47π/18 + 108π/18 = 61π/18.
- 61π/18 is still greater than 2π (36π/18), so subtract 2π: 61π/18 - 36π/18 = 25π/18.
- 25π/18 = π + 7π/18, which is in Quadrant III.
- From the positive x-axis, rotate counterclockwise π (180°), then an additional 7π/18 (70°).
- Terminal side is in Quadrant III, closer to the negative y-axis.
3. For angle 170°:
- Start from the positive x-axis.
- Rotate counterclockwise 170°, which is 10° less than 180°.
- Terminal side is in Quadrant II, very close to the negative x-axis.
4. For angle 510°:
- Reduce by subtracting 360°: 510° - 360° = 150°.
- Start from the positive x-axis.
- Rotate counterclockwise 150°, which is 30° less than 180°.
- Terminal side is in Quadrant II, 30° from the negative x-axis (or 60° from the positive y-axis).
Parent Tip: Review the logic above to help your child master the concept of angles and angle measure.
