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’
Posted on: Sun, 01 Sep 2013 22:10:37 +0000
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