Convert 1,540 degrees to radians.(1 point)

Question

Responses

81π5
radians
Start Fraction 81 pi over 5 End Fraction radians

52π3
radians
Start Fraction 52 pi over 3 End Fraction radians

65π7
radians
Start Fraction 65 pi over 7 End Fraction radians

77π9
radians

Answer 1

To convert degrees to radians, we use the conversion factor \(\frac{\pi \text{ radians}}{180 \text{ degrees}}\).

To convert \(1540\) degrees to radians:

\[ \text{radians} = 1540 \times \frac{\pi}{180} \]

Now, we simplify the fraction:

First, divide \(1540\) by \(180\):

\[ 1540 \div 180 = \frac{1540}{180} = \frac{77}{9} \]

Thus,

\[ \text{radians} = \frac{77}{9} \pi \]

So,

\(\frac{77\pi}{9} \) radians is the final conversion.

The correct response is:

\[ \frac{77\pi}{9} \text{ radians} \]