Question

Convert 1,540 degrees to radians.
A.
5
81π
​
radians B.
3
52π
​
radians C.
7
65π
​
radians D.
9
77π
​
radians

Answer 1

To convert degrees to radians, we use the formula:

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

So, to convert 1,540 degrees to radians:

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

First, simplify \( \frac{1540}{180} \):

\[
\frac{1540}{180} = \frac{154}{18} = \frac{77}{9}
\]

Now, we multiply by \( \pi \):

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

Thus, 1,540 degrees is equal to:

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

Looking at the options provided:

A. \( \frac{5}{81} \pi \) radians
B. \( \frac{3}{52} \pi \) radians
C. \( \frac{7}{65} \pi \) radians
D. \( \frac{9}{77} \pi \) radians

It seems that none of these options correspond to \( \frac{77}{9} \pi \). In fact, the correct answer is:

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

Since that is not provided in the options, please check if the choices given are accurate or complete.