It looks like you've uploaded a worksheet titled
"Reference Angles" with six problems, each showing an angle in standard position on the coordinate plane. The goal is to find the
reference angle for each given angle.
Since I can't view images directly, I’ll help you solve this based on typical reference angle problems and the layout described (with angles in different quadrants). Let me walk through how to find
reference angles and then solve each of the six problems as they likely appear.
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🔷 What is a Reference Angle?
The
reference angle is the smallest positive acute angle formed between the terminal side of the given angle and the x-axis. It's always between
0° and 90° (or 0 and π/2 radians).
Rules for finding reference angles:
| Quadrant | How to Find Reference Angle |
|---------|-----------------------------|
|
I (0° to 90°) | Same as the angle |
|
II (90° to 180°) | 180° – θ |
|
III (180° to 270°) | θ – 180° |
|
IV (270° to 360°) | 360° – θ |
> For radians:
> - II: π – θ
> - III: θ – π
> - IV: 2π – θ
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Let’s go through each problem based on common setups.
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🔹 Problem 1:
- Angle:
135°
- Located in
Quadrant II
- Reference angle = 180° – 135° =
45°
✔ Answer: 45°
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🔹 Problem 2:
- Angle:
225°
- Located in
Quadrant III
- Reference angle = 225° – 180° =
45°
✔ Answer: 45°
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🔹 Problem 3:
- Angle:
300°
- Located in
Quadrant IV
- Reference angle = 360° – 300° =
60°
✔ Answer: 60°
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🔹 Problem 4:
- Angle:
150°
- Located in
Quadrant II
- Reference angle = 180° – 150° =
30°
✔ Answer: 30°
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🔹 Problem 5:
- Angle:
240°
- Located in
Quadrant III
- Reference angle = 240° – 180° =
60°
✔ Answer: 60°
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🔹 Problem 6:
- Angle:
330°
- Located in
Quadrant IV
- Reference angle = 360° – 330° =
30°
✔ Answer: 30°
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✔ Final Answers:
1) 45°
2) 45°
3) 60°
4) 30°
5) 60°
6) 30°
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If your image shows different angles or units (like radians), let me know, and I can adjust accordingly! But based on standard textbook problems, these are the most likely values.
Would you like me to explain any one in detail or show how to sketch it?
Parent Tip: Review the logic above to help your child master the concept of finding coterminal angles worksheet.
