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Convert the radian measure to degrees. Round to the nearest hundredth if necessary.

[tex]\[ -\frac{\pi}{4} \][/tex]

A. [tex]\(-\frac{\pi}{4}\)[/tex]

B. [tex]\(-45 \pi^{\circ}\)[/tex]

C. [tex]\(-45^{\circ}\)[/tex]

D. [tex]\(-0.79^{\circ}\)[/tex]


Sagot :

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.
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