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convert the following angles to degrees minutes and seconds 0.4 and 1.6

 Jul 8, 2014

Best Answer 

 #1
avatar+27529 
+5

To convert from radians (which is what I assume the 0.4 and 1.6 are) to degrees, multiply by 180/pi.

So: 

$${\frac{{\mathtt{0.4}}{\mathtt{\,\times\,}}{\mathtt{180}}}{{\mathtt{\pi}}}} = {\mathtt{22.918\: \!311\: \!805\: \!232\: \!928\: \!4}}$$ 

This is 22° plus 0.9183118...°

There are 60' in 1° so 

$${\mathtt{0.918\: \!311\: \!805\: \!232\: \!928\: \!4}}{\mathtt{\,\times\,}}{\mathtt{60}} = {\mathtt{55.098\: \!708\: \!313\: \!975\: \!704}}$$

This is 55' plus 0.0987...'

There are 60'' in 1' so

$${\mathtt{0.098\: \!708\: \!313\: \!975\: \!704}}{\mathtt{\,\times\,}}{\mathtt{60}} = {\mathtt{5.922\: \!498\: \!838\: \!542\: \!24}}$$

This is 6'' to the nearest second.

Therefore 0.4 radians is 22° 55' 6'' to the nearest second.

 

Now you try converting 1.6 radians.

 Jul 8, 2014
 #1
avatar+27529 
+5
Best Answer

To convert from radians (which is what I assume the 0.4 and 1.6 are) to degrees, multiply by 180/pi.

So: 

$${\frac{{\mathtt{0.4}}{\mathtt{\,\times\,}}{\mathtt{180}}}{{\mathtt{\pi}}}} = {\mathtt{22.918\: \!311\: \!805\: \!232\: \!928\: \!4}}$$ 

This is 22° plus 0.9183118...°

There are 60' in 1° so 

$${\mathtt{0.918\: \!311\: \!805\: \!232\: \!928\: \!4}}{\mathtt{\,\times\,}}{\mathtt{60}} = {\mathtt{55.098\: \!708\: \!313\: \!975\: \!704}}$$

This is 55' plus 0.0987...'

There are 60'' in 1' so

$${\mathtt{0.098\: \!708\: \!313\: \!975\: \!704}}{\mathtt{\,\times\,}}{\mathtt{60}} = {\mathtt{5.922\: \!498\: \!838\: \!542\: \!24}}$$

This is 6'' to the nearest second.

Therefore 0.4 radians is 22° 55' 6'' to the nearest second.

 

Now you try converting 1.6 radians.

Alan Jul 8, 2014

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