Question

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

Answer 1

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

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$\text{(i) -47°30}'$

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

$=\frac{-95}{2} \,degree$

$Since \,180° = π \,radian$

$Since \,180° = π\, radian$

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

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

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

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