How do you convert #232^o7' 57''# to radians?

Question

Victoria Adebayo · Accepted Answer

#232.1325 ( pi/180) radian#

#=4.0515 radian#, nearly.

From degree to radian, the conversion factor is #pi/180# Here, #232^o7'67''# #=(232+7/30+57/3600)^o# #=232.1325^o# #=232.1325 ( pi/180) radian# #=4.0515 radian#, nearly.

Caroline Adams · Answer

undefined To convert $232^\circ 7' 57''$ to radians, we use the conversion factor $1^\circ = \frac{\pi}{180}$ radians and $1'$ (arcminute) is $1/60$ of a degree, and $1''$ (arcsecond) is $1/60$ of an arcminute.

$$232^\circ 7' 57'' = 232^\circ + 7' + 57''$$

$$= 232^\circ + \frac{7}{60}^\circ + \frac{57}{3600}^\circ$$

$$= 232^\circ \times \frac{\pi}{180} + \frac{7}{60}^\circ \times \frac{\pi}{180} + \frac{57}{3600}^\circ \times \frac{\pi}{180}$$

$$= \left(232 + \frac{7}{60} + \frac{57}{3600}\right)^\circ \times \frac{\pi}{180}$$

$$= \left(232 + \frac{7}{60} + \frac{57}{3600}\right) \times \frac{\pi}{180}$$

$$= \left(\frac{13949}{60}\right) \times \frac{\pi}{180}$$

$$= \frac{232.48472222...}{180} \times \pi$$

$$= 1.285891056... \times \pi$$

$$ \approx 4.035 \, \text{radians} $$