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.

Answer 1

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:

$$\boxed{{\displaystyle 5.76}}$$