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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.

       E x a m p l e .  Find a radian measure of an angle 12° 30’ with an of the fourth accuracy
                               decimal place.

       S o l u t i o n .  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° ).

      E x a m p l e .  Find a degree measure of an angle 1.4 rad. with an accuracy up to 1’.

      S o l u t i o n .  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 80°13’.

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