To convert the radian measure [tex]\(-\frac{\pi}{4}\)[/tex] to degrees, follow these steps:
1. Understand the relationship between radians and degrees:
The formula to convert radians to degrees is given by:
[tex]\[
\text{Degrees} = \text{Radians} \times \left(\frac{180}{\pi}\right)
\][/tex]
2. Insert the given radian measure into the formula:
We have the radian measure [tex]\( -\frac{\pi}{4} \)[/tex]. Substitute this value into the conversion formula:
[tex]\[
\text{Degrees} = -\frac{\pi}{4} \times \left(\frac{180}{\pi}\right)
\][/tex]
3. Simplify the expression:
The [tex]\(\pi\)[/tex] terms will cancel each other out:
[tex]\[
\text{Degrees} = -\frac{1}{4} \times 180
\][/tex]
4. Calculate the multiplication:
[tex]\[
\text{Degrees} = -\frac{180}{4} = -45
\][/tex]
So, [tex]\(- \frac{\pi}{4}\)[/tex] radians is equal to [tex]\(-45\)[/tex] degrees.
5. Rounding to the nearest hundredth:
Since [tex]\(-45\)[/tex] is already a whole number, there's no need for further rounding. If it had a decimal component, you would round it to two decimal places.
Thus, the radian measure [tex]\(-\frac{\pi}{4}\)[/tex] converts to [tex]\(-45.00\)[/tex] degrees when rounded to the nearest hundredth.
