What is the value of 45 degrees in radians?

To convert degrees to radians, the formula used is:

[

\text{Radians} = \text{Degrees} \times \left( \frac{\pi}{180} \right)

]

For 45 degrees, the calculation is as follows:

[

45 \times \left( \frac{\pi}{180} \right) = \frac{45\pi}{180}

]

This simplifies down to:

[

\frac{\pi}{4}

]

Thus, the value of 45 degrees in radians is (\frac{\pi}{4}). This conversion accurately reflects the relationship between degrees and radians, where one full rotation (360 degrees) is equivalent to (2\pi) radians, making it essential to simplify fractions correctly.

The other choices do not match this conversion; (\frac{\pi}{2}) would represent 90 degrees, (\frac{3\pi}{4}) corresponds to 135 degrees, and (2\pi) signifies a full rotation of 360 degrees, none of which are accurate for 45 degrees.