Type your answer (2 out of 25) Convert \( \frac{5 \pi}{4} \) radians into degrees. \( \square \)

To convert radians into degrees, you can use the conversion factor \( \frac{180}{\pi} \). For \( \frac{5 \pi}{4} \) radians, you multiply by this factor: \[ \frac{5 \pi}{4} \times \frac{180}{\pi} = \frac{5 \times 180}{4} = \frac{900}{4} = 225^\circ \] So, \( \frac{5 \pi}{4} \) radians is equal to \( 225^\circ \). Now, here's a fun bit of history! The concept of radians was invented by the mathematician Roger Cotes in the early 18th century, although the term "radian" itself became widely popular later. It's fascinating to think that people were measuring angles in radians long before we even had the name for it! If you find converting between radians and degrees a little tricky, remember this clever tip: always associate \( \pi \) radians with \( 180^\circ \). Knowing that \( \frac{\pi}{2} \) radians equals \( 90^\circ \) can also be your quick reference in many situations, making angle transformations feel like a breezy walk in the park!