To solve the problems in the image, we need to convert between degrees and radians. The key relationship between degrees and radians is:
$$
1 \text{ radian} = \frac{180^\circ}{\pi}
$$
This means:
- To convert from radians to degrees: Multiply by $\frac{180}{\pi}$.
- To convert from degrees to radians: Multiply by $\frac{\pi}{180}$.
Let's solve each problem step by step.
---
Problem 1: Convert $\frac{\pi}{7}$ radians to degrees
We use the conversion factor $\frac{180}{\pi}$:
$$
\frac{\pi}{7} \times \frac{180}{\pi} = \frac{180}{7} \approx 25.714^\circ
$$
Answer: $\boxed{25.714^\circ}$
---
Problem 2: Convert $67^\circ$ to radians
We use the conversion factor $\frac{\pi}{180}$:
$$
67^\circ \times \frac{\pi}{180} = \frac{67\pi}{180} \approx 1.17 \text{ radians}
$$
Answer: $\boxed{1.17 \text{ radians}}$
---
Problem 3: Convert $117^\circ$ to radians
We use the conversion factor $\frac{\pi}{180}$:
$$
117^\circ \times \frac{\pi}{180} = \frac{117\pi}{180} = \frac{13\pi}{20} \approx 2.04 \text{ radians}
$$
Answer: $\boxed{2.04 \text{ radians}}$
---
Problem 4: The number of radians in a full circle is approximately ...
A full circle is $360^\circ$. Using the conversion factor $\frac{\pi}{180}$:
$$
360^\circ \times \frac{\pi}{180} = 2\pi \approx 6.28 \text{ radians}
$$
Answer: $\boxed{6.28 \text{ radians}}$
---
Problem 5: Convert $\frac{\pi}{4}$ radians to degrees
We use the conversion factor $\frac{180}{\pi}$:
$$
\frac{\pi}{4} \times \frac{180}{\pi} = \frac{180}{4} = 45^\circ
$$
Answer: $\boxed{45^\circ}$
---
Problem 6: Convert $2\pi$ radians to degrees
We use the conversion factor $\frac{180}{\pi}$:
$$
2\pi \times \frac{180}{\pi} = 2 \times 180 = 360^\circ
$$
Answer: $\boxed{360^\circ}$
---
Problem 7: Convert $127^\circ$ to radians
We use the conversion factor $\frac{\pi}{180}$:
$$
127^\circ \times \frac{\pi}{180} = \frac{127\pi}{180} \approx 2.21 \text{ radians}
$$
Answer: $\boxed{2.21 \text{ radians}}$
---
Final Answers:
1. $\boxed{25.714^\circ}$
2. $\boxed{1.17 \text{ radians}}$
3. $\boxed{2.04 \text{ radians}}$
4. $\boxed{6.28 \text{ radians}}$
5. $\boxed{45^\circ}$
6. $\boxed{360^\circ}$
7. $\boxed{2.21 \text{ radians}}$
---
Boxed Final Answer:
$$
\boxed{25.714^\circ, 1.17 \text{ radians}, 2.04 \text{ radians}, 6.28 \text{ radians}, 45^\circ, 360^\circ, 2.21 \text{ radians}}
$$
Parent Tip: Review the logic above to help your child master the concept of radian to degree worksheet.
