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In this part, convert degrees to radians. Your answer will be a fully reduced fraction (or integer) times [tex]\pi[/tex]. You only need to enter the fraction, as I have provided the [tex]\pi[/tex]. Write your answer using [tex]/[/tex], such as [tex]5 / 9[/tex].

[tex]
-180^{\circ} = \square \pi
[/tex]

[tex]
125^{\circ} = \square \pi
[/tex]


Sagot :

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]