Convert 12pi/17 radians to degree measure. And convert 116 degrees to radian measure. Round answers to the nearest hundreth

To convert between radians and degrees, we use the following conversion factors:

- \( 1 \, \text{radian} = \dfrac{180}{\pi} \, \text{degrees} \)
- \( 1 \, \text{degree} = \dfrac{\pi}{180} \, \text{radians} \)

### 1. Convert \( \dfrac{12\pi}{17} \) radians to degrees:

\[
\text{Degrees} = \dfrac{12\pi}{17} \times \dfrac{180}{\pi}
\]
The \(\pi\) terms cancel out, and we simplify:

\[
\text{Degrees} = \dfrac{12 \times 180}{17} = \dfrac{2160}{17} \approx 127.06^\circ
\]

### 2. Convert 116 degrees to radians:

\[
\text{Radians} = 116^\circ \times \dfrac{\pi}{180}
\]

Simplifying:

\[
\text{Radians} = \dfrac{116 \pi}{180} = \dfrac{29 \pi}{45} \approx 2.02 \, \text{radians}
\]

### Final Results:
- \( \dfrac{12\pi}{17} \, \text{radians} \approx 127.06^\circ \)
- \( 116^\circ \approx 2.02 \, \text{radians} \)

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Here are 5 related questions to extend this topic:
1. How would you convert 300 degrees to radians?
2. What is \( \pi/3 \) radians in degrees?
3. How many radians are there in a full circle?
4. Convert 45 degrees to radians and 90 degrees to radians.
5. Why is \( \pi \) radians equivalent to 180 degrees?

**Tip:** Always remember that \( \pi \, \text{radians} = 180^\circ \), and use this as the basis for conversions between radians and degrees.

Convert 12pi/17 radians to degree measure. And convert 116 degrees to radian measure. Round answers to the nearest hundredth.

Learn how to convert 12π/17 radians to degrees and 116 degrees to radians with step-by-step solutions. This problem demonstrates how to apply key trigonometric conversion formulas, with results rounded to the nearest hundredth. Suitable for Grades 9-12.

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