To find a
coterminal angle between 0° and 360°, we add or subtract multiples of
360° to the given angle until the result is within the desired range:
>
0° ≤ angle < 360°
Coterminal angles are angles that share the same terminal side (i.e., they point in the same direction) when drawn in standard position.
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Let’s solve each one:
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1) –150°
We add 360° to get into the 0°–360° range:
> –150° + 360° =
210°
✔ Answer: 210°
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2) –260°
Add 360°:
> –260° + 360° =
100°
✔ Answer: 100°
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3) 550°
This is greater than 360°, so subtract 360°:
> 550° – 360° =
190°
✔ Answer: 190°
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4) 860°
Subtract 360° repeatedly until in range:
> 860° – 360° = 500°
> 500° – 360° =
140°
✔ Answer: 140°
*(Alternatively: 860 ÷ 360 ≈ 2.388 → subtract 2×360 = 720 → 860 – 720 = 140°)*
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5) –284°
Add 360°:
> –284° + 360° =
76°
✔ Answer: 76°
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6) 391°
Subtract 360°:
> 391° – 360° =
31°
✔ Answer: 31°
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7) –395°
Add 360° once:
> –395° + 360° = –35° → still negative, so add 360° again:
> –35° + 360° =
325°
✔ Answer: 325°
*(Alternatively: –395 + 2×360 = –395 + 720 = 325°)*
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##
✔ Final Answers:
1)
210°
2)
100°
3)
190°
4)
140°
5)
76°
6)
31°
7)
325°
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## 📌 Summary:
- For
negative angles: keep adding 360° until you’re ≥ 0°.
- For
angles ≥ 360°: keep subtracting 360° until you’re < 360°.
- The goal is always to land in the interval
[0°, 360°).
These are all coterminal with the original angles — meaning they point in the exact same direction on the unit circle.
Parent Tip: Review the logic above to help your child master the concept of reference angles worksheet.
