https://file.aiquickdraw.com/mathbot/file/1726453104599q0tn1aep.jpg

To convert degrees to radians, we use the formula:

\[
\text{radians} = \frac{\pi}{180^\circ} \times \text{degrees}
\]

Let's solve the two problems:

### Problem 11: Convert \(145^\circ\) to radians
\[
\text{radians} = \frac{\pi}{180^\circ} \times 145^\circ = \frac{145\pi}{180}
\]

Simplifying the fraction:
\[
\frac{145\pi}{180} = \frac{29\pi}{36}
\]

In decimal form:
\[
\frac{29\pi}{36} \approx 2.5307
\]

### Problem 12: Convert \(510^\circ\) to radians
\[
\text{radians} = \frac{\pi}{180^\circ} \times 510^\circ = \frac{510\pi}{180}
\]

Simplifying the fraction:
\[
\frac{510\pi}{180} = \frac{17\pi}{6}
\]

In decimal form:
\[
\frac{17\pi}{6} \approx 8.902
\]

### Answers:
- \(145^\circ\) in radians is \(\frac{29\pi}{36}\) or approximately 2.5307.
- \(510^\circ\) in radians is \(\frac{17\pi}{6}\) or approximately 8.902.

Would you like further details on the conversion process?

Here are some related questions to explore:
1. What is the formula for converting radians back to degrees?
2. How would you simplify a different degree measure to radians?
3. Why is \( \pi \) used in radian conversion?
4. How do radian measures relate to the unit circle?
5. What is the radian measure of common angles like \(30^\circ\), \(60^\circ\), and \(90^\circ\)?

**Tip**: Always simplify fractions when converting to radians for clearer results.

Convert 145° and 510° to radian measure, in both π form and decimal form.

Learn how to convert the angles 145° and 510° to radians using the angle conversion formula. See detailed steps for converting degrees to radians in both π form and decimal form, suitable for high school trigonometry students.

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