Certainly! Let's convert the degree measurement [tex]\(126^\circ\)[/tex] to radians and express the answer as a multiple of [tex]\(\pi\)[/tex].
1. Understand the Relationship Between Degrees and Radians:
The conversion from degrees to radians is done using the following relationship:
[tex]\[
1\text{ degree} = \frac{\pi}{180}\text{ radians}
\][/tex]
Therefore, to convert [tex]\(126^\circ\)[/tex] to radians, we use the formula:
[tex]\[
\text{radians} = \text{degrees} \times \frac{\pi}{180}
\][/tex]
2. Apply the Conversion:
Plugging [tex]\(126^\circ\)[/tex] into the formula:
[tex]\[
\text{radians} = 126 \times \frac{\pi}{180} = \frac{126\pi}{180}
\][/tex]
3. Simplify the Fraction:
Simplify the fraction [tex]\(\frac{126\pi}{180}\)[/tex]:
[tex]\[
\frac{126\pi}{180} = \frac{126}{180} \pi
\][/tex]
First, find the greatest common divisor (GCD) of 126 and 180, which is 18.
[tex]\[
\frac{126 \div 18}{180 \div 18} = \frac{7}{10}
\][/tex]
Therefore, we have:
[tex]\[
\frac{126\pi}{180} = \frac{7\pi}{10}
\][/tex]
4. Conclusion:
The given degree measurement [tex]\(126^\circ\)[/tex] is equivalent to [tex]\(\frac{7\pi}{10}\)[/tex] radians.
Thus, the correct answer is:
[tex]\[
\boxed{\frac{7 \pi}{10}}
\][/tex]
