Question

Find the radian measures corresponding to the following degree measures (i) 25° (ii) - 47° 30' (iii) 240° (iv) 520°

Answer 1

\(\text{(i) 25°}\)
\(\text{We\, know\, that\, 180° = π\, radian}\)
\(∴ 25° = \frac{π}{180} × 25\,radian = \frac{5π }{36} \,radian\)

---

\(\text{(i) -47°30}'\)

\(–47° 30' -47\frac{1}{2}\,\,degree \,[1° = 60']\) 

\(=\frac{-95}{2} \,degree\)

\(Since \,180° = π \,radian\)

\(Since \,180° = π\, radian\)

\(\frac{-95}{2} \,degree = \frac{π}{180}×(\frac{-95}{2})\,radian = (\frac{-19}{36 × 2}) π \,radian = \frac{-19}{72 }π \,radian\)

\(∴ -47° 30' = -\frac{19}{72} π\,radian\) 

---

\(\text{(iii) 240°}\)
\(\text{We \,know \,that \,180° = π \,radian}\)
\(∴ 240° = \frac{π}{180}×240 \,radian = \frac{4}{3}π \,radian\)

---

\(\text{(iv) 520°}\)
\(\text{We\, know\, that \,180° = π\, radian}\)
\(∴ 520° = \frac{π}{180}×520 \,radian = \frac{26π}{9} \,radian\)