Convert X, Y Rotation coordinates from Radians to Degrees

Question

I have 2 values that are in radians, c[1] and c[3]. I need to turn the radians into degrees and I haven't the faintest idea what to do to these numbers to get degrees out of them. I have been searching the internet far and wide and I cant find anything that I can actually understand. I have tried devising my own way to do it but I'm sure I'm not even close. I have tried the following:

    z = (((c[1] * 180) + 180) + ((c[3] * 180) + 180))
    z = (((c[1] * math.pi) / 180) + ((c[3] * math.pi) / 180) / 2)
    z = (c[1] * (90/math.pi) - (c[3] * (90/math.pi)))
    z = math.atan2(c[3], c[1])
    z = (math.degrees(c[1]) + math.degrees(c[3])) * 2
    z = c[1]
    z = (math.asin(c[3]) / math.acos(c[1]))

How do I get a value in degrees from 2 radians?

Answer 1

After going through your comment, I don't think that you are getting two angles in radians for c[1] and c[3]. Rather, you are getting direction cosines. If you were getting angles in radians, the value would range from -pi to pi. Rather, the value goes from -1 to 1 (i.e. cos(-pi) to cos(pi)).

You can change the value first to an angle in radians and then to degrees if that is what you want. Just as a caveat, the cosine of angles is symmetric ... So for:

In [12]: zip(angles, (cos(angles)))
Out[12]:
[(-3.1415926535897931, -1.0),
 (-2.8108986900540254, -0.94581724170063464),
 (-2.4802047265182576, -0.78914050939639346),
 (-2.1495107629824899, -0.5469481581224267),
 (-1.8188167994467224, -0.24548548714079912),
 (-1.4881228359109546, 0.082579345472332394),
 (-1.1574288723751871, 0.40169542465296937),
 (-0.82673490883941936, 0.67728157162574099),
 (-0.49604094530365161, 0.87947375120648907),
 (-0.16534698176788387, 0.98636130340272232),
 (0.16534698176788387, 0.98636130340272232),
 (0.49604094530365161, 0.87947375120648907),
 (0.82673490883941891, 0.67728157162574132),
 (1.1574288723751867, 0.40169542465296976),
 (1.4881228359109544, 0.082579345472332616),
 (1.8188167994467221, -0.2454854871407989),
 (2.1495107629824899, -0.5469481581224267),
 (2.4802047265182576, -0.78914050939639346),
 (2.8108986900540254, -0.94581724170063464),
 (3.1415926535897931, -1.0)]

But,

In [11]: zip(angles, arccos(cos(angles)))
Out[11]:
[(-3.1415926535897931, 3.1415926535897931),
 (-2.8108986900540254, 2.8108986900540254),
 (-2.4802047265182576, 2.4802047265182576),
 (-2.1495107629824899, 2.1495107629824899),
 (-1.8188167994467224, 1.8188167994467224),
 (-1.4881228359109546, 1.4881228359109546),
 (-1.1574288723751871, 1.1574288723751871),
 (-0.82673490883941936, 0.82673490883941936),
 (-0.49604094530365161, 0.49604094530365156),
 (-0.16534698176788387, 0.16534698176788418),
 (0.16534698176788387, 0.16534698176788418),
 (0.49604094530365161, 0.49604094530365156),
 (0.82673490883941891, 0.82673490883941891),
 (1.1574288723751867, 1.1574288723751867),
 (1.4881228359109544, 1.4881228359109544),
 (1.8188167994467221, 1.8188167994467221),
 (2.1495107629824899, 2.1495107629824899),
 (2.4802047265182576, 2.4802047265182576),
 (2.8108986900540254, 2.8108986900540254),
 (3.1415926535897931, 3.1415926535897931)]

Which means that getting your angles from your direction cosines, you will need to do:

In [13]: def toAng(a): return sign(a)*arccos(a)

which will give you your correct angles:

In [19]: zip(angles, toAng(cos(angles)))
Out[19]:
[(-3.1415926535897931, -3.1415926535897931),
 (-2.8108986900540254, -2.8108986900540254),
 (-2.4802047265182576, -2.4802047265182576),
 (-2.1495107629824899, -2.1495107629824899),
 (-1.8188167994467224, -1.8188167994467224),
 (-1.4881228359109546, 1.4881228359109546),
 (-1.1574288723751871, 1.1574288723751871),
 (-0.82673490883941936, 0.82673490883941936),
 (-0.49604094530365161, 0.49604094530365156),
 (-0.16534698176788387, 0.16534698176788418),
 (0.16534698176788387, 0.16534698176788418),
 (0.49604094530365161, 0.49604094530365156),
 (0.82673490883941891, 0.82673490883941891),
 (1.1574288723751867, 1.1574288723751867),
 (1.4881228359109544, 1.4881228359109544),
 (1.8188167994467221, -1.8188167994467221),
 (2.1495107629824899, -2.1495107629824899),
 (2.4802047265182576, -2.4802047265182576),
 (2.8108986900540254, -2.8108986900540254),
 (3.1415926535897931, -3.1415926535897931)]

Finally, if you need to convert it to degrees, you can just do:

In [20]: def toAng(a): return 180*sign(a)*arccos(a)/pi

In [21]: zip(angles, toAng(cos(angles)))
Out[21]:
[(-3.1415926535897931, -180.0),
 (-2.8108986900540254, -161.05263157894737),
 (-2.4802047265182576, -142.10526315789474),
 (-2.1495107629824899, -123.1578947368421),
 (-1.8188167994467224, -104.21052631578948),
 (-1.4881228359109546, 85.263157894736835),
 (-1.1574288723751871, 66.31578947368422),
 (-0.82673490883941936, 47.368421052631582),
 (-0.49604094530365161, 28.421052631578949),
 (-0.16534698176788387, 9.4736842105263346),
 (0.16534698176788387, 9.4736842105263346),
 (0.49604094530365161, 28.421052631578949),
 (0.82673490883941891, 47.368421052631554),
 (1.1574288723751867, 66.315789473684191),
 (1.4881228359109544, 85.263157894736835),
 (1.8188167994467221, -104.21052631578947),
 (2.1495107629824899, -123.1578947368421),
 (2.4802047265182576, -142.10526315789474),
 (2.8108986900540254, -161.05263157894737),
 (3.1415926535897931, -180.0)]

Which gives you the right angles in degrees ...

Note I am using an environment where sign, pi etc are numpy objects. In your program, you might have ti import them separately.

Answer 2

degree to radian conversions are done with the equation (n deg)*(pi/180 deg).

z = (c[1]*(math.pi/180.0) + (c[1]*(math.pi/180)

if it's something you need to do regularly make a function.

def DegtoRad(deg):
    return (deg)*(math.pi/180)

or as a lambda

DegtoRad = lambda x: x*(math.pi/180)

remember though if you havent imported math/math.pi none of this will work. probably better to define pi with an actual literal variable up to your needs of precision.

Answer 3

This was not so very hard to find online? - was it?

http://www.mathwarehouse.com/trigonometry/radians/convert-degee-to-radians.php

The formula is the opposite of @user2913685 's formula: num*180/pi (an easy mistake)

here is an example in python:

pi = 3.14159265

rad_val = 7

deg_val = rad_val*180/pi

print(deg_val)

which gives the output:

401.07045704986604

This uses pi as 3.14159265, and doesn't use the module math. Obviously you can do the same as in the other answer, but after changing the formula.