Convert \( 45^\circ \) to radians.

Convert \( 45^\circ \) to radians.

• A. \(\frac{\pi}{2}\)
• B. \(\frac{\pi}{4}\)
• C. \(\frac{\pi}{3}\)
• D. \(\frac{\pi}{6}\)

Answer: (B)

To convert degrees to radians, we use the conversion factor that \( \pi \) radians is equivalent to \( 180^\circ \). The formula for conversion is: \[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \] Applying this formula for \( 45^\circ \): \[ \text{radians} = 45 \times \frac{\pi}{180} \] Now, simplifying the fraction: \[ \frac{45}{180} = \frac{1}{4} \] So we have: \[ \text{radians} = \frac{1}{4} \pi = \frac{\pi}{4} \] Thus, \( 45^\circ \) is correctly converted to \( \frac{\pi}{4} \) radians, which is why this is the correct answer.

To convert degrees to radians, we use the conversion factor that ( \pi ) radians is equivalent to ( 180^\circ ). The formula for conversion is:

[

\text{radians} = \text{degrees} \times \frac{\pi}{180}

]

Applying this formula for ( 45^\circ ):

[

\text{radians} = 45 \times \frac{\pi}{180}

]

Now, simplifying the fraction:

[

\frac{45}{180} = \frac{1}{4}

]

So we have:

[

\text{radians} = \frac{1}{4} \pi = \frac{\pi}{4}

]

Thus, ( 45^\circ ) is correctly converted to ( \frac{\pi}{4} ) radians, which is why this is the correct answer.