Answer :
To convert degrees to radians, we use the formula:
[tex]\[ \text{radians} = \text{degrees} \times \left(\frac{\pi}{180}\right) \][/tex]
Let's apply this formula for each angle:
1. Converting \(-180^\circ\) to radians:
[tex]\[ -180^\circ \times \left(\frac{\pi}{180}\right) = -\frac{180}{180} \pi = -1 \pi \][/tex]
Thus, \(-180^\circ = -1 \pi\).
2. Converting \(125^\circ\) to radians:
[tex]\[ 125^\circ \times \left(\frac{\pi}{180}\right) = \frac{125}{180} \pi \][/tex]
Now we simplify the fraction \(\frac{125}{180}\):
First, determine the greatest common divisor (GCD) of 125 and 180. The GCD is 5.
[tex]\[ \frac{125 \div 5}{180 \div 5} = \frac{25}{36} \][/tex]
Thus, \(125^\circ = \frac{25}{36} \pi\).
So, the final answers are:
[tex]\[ -180^\circ = -1 \][/tex]
[tex]\[ 125^\circ = \frac{25}{36} \][/tex]
[tex]\[ \text{radians} = \text{degrees} \times \left(\frac{\pi}{180}\right) \][/tex]
Let's apply this formula for each angle:
1. Converting \(-180^\circ\) to radians:
[tex]\[ -180^\circ \times \left(\frac{\pi}{180}\right) = -\frac{180}{180} \pi = -1 \pi \][/tex]
Thus, \(-180^\circ = -1 \pi\).
2. Converting \(125^\circ\) to radians:
[tex]\[ 125^\circ \times \left(\frac{\pi}{180}\right) = \frac{125}{180} \pi \][/tex]
Now we simplify the fraction \(\frac{125}{180}\):
First, determine the greatest common divisor (GCD) of 125 and 180. The GCD is 5.
[tex]\[ \frac{125 \div 5}{180 \div 5} = \frac{25}{36} \][/tex]
Thus, \(125^\circ = \frac{25}{36} \pi\).
So, the final answers are:
[tex]\[ -180^\circ = -1 \][/tex]
[tex]\[ 125^\circ = \frac{25}{36} \][/tex]
