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Transforming of degree measure to radian one and back
1. To find a radian measure of any angle by its given degree measure it is necessary to multiply: a number of degrees by / 180 ? 0.017453, a number of minutes – by / (180 · 60 ) ? 0.000291, a number of seconds – by / (180 · 60 · 60 ) ? 0.000005 and to add the found products.

Example: Find a radian measure of an angle 12° 30’ with an of the fourth accuracy decimal place.

Solution:
Multiply 12 by / 180 : 12 · 0.017453 ? 0.2094.
Multiply 30 by / (180 · 60 ) : 30 · 0.000291 ? 0.0087.
Now we find:
12°30’ ? 0.2094 + 0.0087 = 0.2181 rad.
2. To find a degree measure of any angle by its given radian measure it is necessary to multiply a number of radians by 180° / ? 57°.296 = 57°17’45” ( a relative error of the result will be ~ 0.0004%, that corresponds to an absolute error ~ 5” for a round angle 360° ).

Example: Find a degree measure of an angle 1.4 rad. with an accuracy up to 1’.

Solution:
We’ll find consequently:
1 rad ? 57°17’45” ;
0.4 rad ? 0.4 · 57°.296 = 22°.9184;
0°.9184 · 60 ? 55’.104;
0’.104 · 60 ? 6”.
So, 0.4 rad 22°55’6” and hence:

1 rad ? 57°17’45”
+
0.4 rad ? 22°55’6”
_____________________
1.4 rad ? 80°12’51”

After rounding this result according to the required accuracy up to 1’ we have finally: 1.4 rad ? s80°13’.

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