I see the diff between Radians and Degrees as, according to the above formula 1 Radian = 57.3 Degrees BUT if I use a scientific calculator, the ratio between a Sine(x) in Radians and a Sine(x) in Degrees is never 57.3 If I process in C# Math.sin(x), I get an answer in Radians, but mutiplying that answer by 57.3 gives a different outcome to that on a calculator. What am I missing?
@George: Thanks for the comment! Yep, you can see radians as a ratio between the distance traveled on the circle and the radius.
@azariah007: Glad you’re able to find it useful --after a while you might see radians starting to make sense :).
@Dave: Great question. Radians -> degree conversions need to happen when you’re inputting the angle; after you’ve run sin, the result will be vastly different.
So, you can say
sin(d) = sin®
where d = 57.3 * r. So, you could pick r = 1 (and d = 57.3) and get the same result.
Math is soooooooooooooooo interesting to me with the numbers and the signs and the stuff that makes numbers make sense. Ahhhhh amazinggggg!!! (SMILING REAL BIGG)
You could say that I am a bit lazy when it comes to posting comments - but to miss a chance to say how great this is would be too much to lose
@Milos: Thanks!
Thank you for your explanation, it made a lot more sense than the others I’ve seen (which basically just say “It’s a radian. Get over it.” but in a posher way.)
The only thing which is still niggling away at me is that 57 degrees does not divide into 360 degrees neatly. I mean, one foot is 12 inches, not 11.67 inches. I find that ugly, but I guess it is all part of the wonderful mystery of pi.
What an excellent article! I’m currently studying trigonometry at school and Radians didn’t make sense to me. However, now I understand them much better.
[…] (a radian is used for trigonometry), but instead to understand them, realize why they were created (a radian is the distance traveled divided by the radius of a circle). This is my aspiration in life, what I wish to accomplish: I want to understand all that I can of […]
Dear Kalid,
I have lots of difficulties understanding solid angles (steradians). For starters, I don’t see how it can be a ratio since it’s an area divided by a length. Furthurmore, I want to know how to calculate solid angles in a 3 dimensional model, but I simply don’t understand many of the explanations provided on the net. I hope you can clear my doubts on this subject.
Yours faithfully,
Aadit M Shah
[…] we need to keep in mind. First, when we compute arctangent(offY / offX), the result will be in radians, while Cocos2D deals with degrees. Luckily, Cocos2D provides an easy to use conversion macro we can […]
difficult to understrand in less time
Hello Khalid,
[…] for "pi" units of time means going pi radians around a […]
useless crap
i hate this thing
In high-school, when my teacher was attempting to teach the trigonometry required for basic calculus, I had NO IDEA what radians are.
And then, in a trig book on the internet recently, I saw the explanation: a radian is a what you get when the length of the segment of the circle’s circumference being measured is equal to the length of the radius.
Click!
My immediate reaction was: “Oh. That makes a lot of sense. It simplifies the measuring of angles to the measuring of circumferences.” And it felt a lot more elegant and useful.
THAT is the feeling of why I love math.
@Dave: Awesome comment – that’s exactly it. One thing I didn’t realize: Suppose I asked you to give me a 37 degree angle. How would you do it? Without tools or a calculator (for fun sine/cosine tricks), you’d have to guesstimate (hrm, I know 45 degrees, maybe I can do a little less).
But, if I said “Create an angle of 0.5 radians” it’d be straightforward. Take some amount of string, attach it to a pencil, and draw a circle. Then take half of that (0.5) and begin wrapping it around the circumference – whereever it ends is 0.5 radians.
There are probably much better ways to construct it, but it really helps it click when you realize how hard angles are to draw without external tools.
this is another thank you message,
this actually helped me understand how exactly mathematics works, i mean the other day i read somewhere about how easier arithmetic would be if we used base 12 rather then 10, and this post came to mind. maybe 100 years from now when computer processing power comes to stagnation we will look for ways to improve our thinking efficiency and say hey base 12, and in no time kids with be struggling to memorize tables in base 12. the same way some mathematics wrote 500 years ago about how easier it would make trig if we used radians but no one cared until we had to calculate angular velocities and stuffs.
@Joy: Heh, a lot of it is based on your reference point for sure. I can’t imagine trying to do math in the days of Roman numerals – once we find a better model (like decimal numbers) the old system seems so antiquated.
thanks for this article! it’s a big help for me…