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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 â€“ by / (180 Â· 60 ) ? 0.000291, a number of seconds â€“ by / (180 Â· 60 Â· 60 ) ? 0.000005 and to add the found products.

Example: Find a radian measure of an angle 12Â° 30â€™ with an of the fourth accuracy decimal place.

Solution:
Multiply 12 by / 180 : 12 Â· 0.017453 ? 0.2094.
Multiply 30 by / (180 Â· 60 ) : 30 Â· 0.000291 ? 0.0087.
Now we find:
12Â°30â€™ ? 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 180Â° / ? 57Â°.296 = 57Â°17â€™45â€ ( a relative error of the result will be ~ 0.0004%, that corresponds to an absolute error ~ 5â€ for a round angle 360Â° ).

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

Solution:
Weâ€™ll find consequently:
0.4 rad ? 0.4 Â· 57Â°.296 = 22Â°.9184;
0Â°.9184 Â· 60 ? 55â€™.104;
0â€™.104 Â· 60 ? 6â€.
So, 0.4 rad 22Â°55â€™6â€ and hence: View My Stats Privacy Statement © 2006 MathPlusFun, All Rights Reserved