I am using Numpy's trigonometric functions, and I just found something intriguing: I know that the sine and cosine functions have an infinite domain, but for some reasons np.cos() and np.sin() don't seem to. When I ask for angles out of [0, 2π], things start to get interesting: np.sin(0) Out[26]: 0.0 np.sin(np.pi) Out[27]: 1.2246467991473532e-16 np.sin(2 * np.pi) Out[28]: -2.4492935982947064e-16 np.sin(3 * np.pi) Out[29]: 3.6739403974420594e-16 np.sin(4 * np.pi) Out[30]: -4.898587196589413e-16 np.sin(12000 * np.pi) Out[31]: -2.038010347584904e-12 It goes similarly with the cosine function, and the bigger the input angle gets, the higher the error will be. np.sin(1e60*np.pi) Out[32]: 0.19270788453190046 Now, I understand that a computer cannot perform high precision calculus when it comes to trigonometry, but is there a way to maintain this initial [0, 2π[ precision? Maybe some libraries that include a simple function like this: from numpy import pi # Just in order to keep it simple π = pi def sin(x): # If our angle is bigger than 360° if x >= 2*π: while x >= 2*π: x -= 2*π # If our angle is smaller than 0° elif x < 0: while x < 0: x += 2*π # If our angle is in [0, 2*π[ domain <act normally as Numpy> return result Is it something that wouldn't work, from a mathematical point of view? Why? Continue reading...
