trigonometry

I'm doing some trigonometry calculations in C/C++ and am running into problems with rounding errors. For example, on my Linux system: #include <stdio.h> #include <math.h> int main(int argc, char *argv[]) { printf("%e\n", sin(M_PI)); return 0; } This program gives the following output: 1.224647e-16 when the correct answer is of course 0. How much rounding error can I expect when using trig functions? How can I best handle that error? I'm familiar with the Units in Last Place technique for comparing floating point numbers, from Bruce Dawson's Comparing Floating Point Numbers , but that doesn't

I have a task to draw a specific graphic. As part of this task I need to rotate some dot's on 45 degrees. I've spent already 2 days trying to calculate a formula, but just couldn't get it right. I've been searching all over the place including this particular website, I'm getting very close, but I'm still not there. Here it is: I need to draw 4 different points I have a specific formula to calculate there position, which is out of scope of the question, but here is what I'm getting as a result of it: int radius = 576; int diameter = radius * 2; Point blueA = new Point(561, 273); Point greenB =

What's the simplest way to generate a sine wave sound at any frequency in Java? A sample size more than 2 bytes would help, but it doesn't really matter. Thanks Andrew Thompson See Beeper for a self-contained example. Perhaps something simpler? That 51 lines of snippet (repeated below - spaced out for single line & in-line comments) as shown at the top of the linked answer, is about as simple as generating a tone gets (OK, you can take out 5+ lines for the harmonic). People seem to assume it should be a method built into the toolkit to produce a pure tone. It is not, and takes a little

I run into this occasionally and always forget how to do it. One of those things that pop up ever so often. Also, what's the formula to convert angles expressed in radians to degrees and back again? Dave Costa radians = degrees * (pi/180) degrees = radians * (180/pi) As for implementation, the main question is how precise you want to be about the value of pi. There is some related discussion here a complete circle in radians is 2*pi. A complete circle in degrees is 360. To go from degrees to radians, it's (d/360) * 2*pi, or d*pi/180. x rads in degrees - > x*180/pi x degrees in rads -> x*pi/180

I have a simple animation in Java that consists of a wheel moving across a window. It is just a plain circle that starts off of the screen from the left, enters and continues to the right until it goes off of the screen. Then it loops and repeats this process. X is a variable that contains the position of the wheel. It can be between -(wheel width) and the window size + the wheel width. I would like to simulate rotation by drawing a circle within this wheel, that rotates around the circle as if it were attached. Imagine a bike wheel in real life with a red flag on the wheel. As the wheel

I've got a little Problem with the Math.cos() method. I know, I have to convert the angle to Radians before using Math.cos() . But if I just do: System.out.println(Math.cos(Math.toRadians(90)); It outputs: 6.123233995736766E-17 Math.sin() is working well. From trigonometry: sin x ~= x, for small values of x sin x = cos x+pi/2 Because pi/2 can't be represented exactly in IEEE-754 Floating point, it means, that it must be off by some value x, i.e it is represented by pi/2 +- x, where x < the least significant bit in the floating point system. Which in this case is 2^-53 = 1.1102e-16. In this