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

1 Answer
May 19, 2015

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