coterminal angles degree and radian worksheet

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23-11-2024

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Meta Description: Master coterminal angles! This comprehensive worksheet covers finding coterminal angles in both degrees and radians, with examples, practice problems, and solutions. Perfect for students learning trigonometry.

Understanding Coterminal Angles

Coterminal angles are angles that share the same terminal side when drawn in standard position. In simpler terms, imagine spinning around a circle; coterminal angles end up pointing in the exact same direction. They differ by a multiple of 360 degrees (or 2π radians).

Finding Coterminal Angles in Degrees

To find a coterminal angle in degrees, add or subtract multiples of 360° to the given angle.

Example: Find a coterminal angle to 50°.

Adding 360°: 50° + 360° = 410°

Subtracting 360°: 50° - 360° = -310°

Therefore, 410° and -310° are coterminal with 50°.

Finding Coterminal Angles in Radians

The process is similar for radians, but instead of 360°, we add or subtract multiples of 2π radians.

Example: Find a coterminal angle to π/3 radians.

Adding 2π: π/3 + 2π = 7π/3

Subtracting 2π: π/3 - 2π = -5π/3

Thus, 7π/3 and -5π/3 are coterminal with π/3.

Coterminal Angles Worksheet: Practice Problems

This section provides practice problems to solidify your understanding. Remember to show your work!

Instructions: Find two coterminal angles (one positive and one negative) for each given angle.

Part 1: Degrees

1. 100°
2. -20°
3. 450°
4. 780°
5. -135°

Part 2: Radians

1. π/4
2. 2π/3
3. 5π/6
4. -π/2
5. 7π

Part 3: Mixed Practice (Degrees and Radians)

1. 150°
2. 3π/2
3. -30°
4. 11π/6
5. 900°

Solutions to Practice Problems

Part 1: Degrees

1. 460°, -260°
2. 340°, -580°
3. 80°, -280°
4. 180°, -180°
5. 225°, -495°

Part 2: Radians

1. 9π/4, -7π/4
2. 8π/3, -4π/3
3. 17π/6, -7π/6
4. 3π/2, -5π/2
5. π, -π

Part 3: Mixed Practice (Degrees and Radians)

1. 510°, -210°
2. π/2, -π/2
3. 330°, -570°
4. 5π/6, -19π/6
5. 180°, -180°

Advanced Coterminal Angle Problems

Question: How many coterminal angles exist for any given angle?

Answer: Infinitely many. You can add or subtract multiples of 360° (or 2π radians) infinitely many times.

Question: Find the smallest positive coterminal angle for -750°.

Answer: -750° + 2(360°) = -750° + 720° = -30°. Since we are looking for the smallest positive, we add another 360°: -30° + 360° = 330°.

Conclusion

Understanding coterminal angles is a foundational concept in trigonometry. This worksheet provides a solid base for mastering this skill, allowing you to confidently tackle more complex trigonometric problems. Remember to practice regularly, and don't hesitate to review the examples and solutions. By consistently practicing, you'll become proficient in identifying coterminal angles in both degrees and radians.