Convert 330-degree measure to radian measure. Type answer as an integer or decimal. Do not round until the final answer. Then round to the nearest hundredth as needed.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

To convert degrees to radians, you can use the formula:

\[ \text{radians} = \text{degrees} \times \left( \frac{\pi}{180} \right) \]

For 330 degrees:

\[ \text{radians} = 330 \times \left( \frac{\pi}{180} \right) = \frac{330\pi}{180} \]

Now, simplify the fraction:

\[ \frac{330}{180} = \frac{11}{6} \]

Thus,

\[ \text{radians} = \frac{11\pi}{6} \]

To get a decimal approximation, we can calculate this value using \(\pi \approx 3.141592653589793\):

\[ \text{radians} \approx \frac{11 \times 3.141592653589793}{6} \approx 5.759586531581287 \]

Now, rounding to the nearest hundredth:

\[ 5.759586531581287 \approx 5.76 \]

So the final answer in radians, rounded to the nearest hundredth, is:

\[ \boxed{5.76} \]