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, $145º51'21''=-0.8103pi$