How do you convert -149 degrees 51 mins 21 secs degrees into radians?

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Answer 1 · 2015-05-19T01:53:11

We know that #360º0'0''=2pi#

So, #-149º51'21''=x#

Let's just cross-mutiply:

#(360º)/(-149º51'21'')=(2pi)/x#

We know, however, that #1'=60''# and that #60'=1º#.

Thus, let's transform it all into seconds.

#360º=360*60*60=1296000''#
#145º=145*60*60=522000''#
#51'=51*60=3060#

Thus, #-145º51'21''=-(522000+3060+21)=-525081''#

Now, we can continue.

#1296000/(-525081)=(2pi)/x#

#x=((2pi)(-525081))/1296000=-0.8103pi#

So, #145º51'21''=-0.8103pi#