Hi Guys, I was wondering how one would write a C program that calculates the value of a cosine function without using any library functions from <math.h>
I need the outputs to turn out like this
Case 1: cos(-1.000) = 0.540302303792
Case 2: cos(1.000) = 0.540302303792
Case 3: cos(1.500) = -0.125000000000
Case 4: cos(2.000) = -0.422222222222
Case 5: cos(2.000) = 1.000000000000
Jump to PostHis assignment, which he posted here, states that he is suppose to use the given Taylor series expansion.
What came to my mind was that you can try interpolating a couple of points along the radians-axis like x = {(-3*pi), (-2*pi), -pi, 0, pi, (2*pi), (3*pi)} and the known cosine values; y = { 0, -1, 0, 1, 0, -1, 0 } . Now I'm using 7 points, but the more points you utilize the more precise your cosine curve will be when close to origo. This curve can be calculated beforehand (maybe look for the polynom ( cosPoly(x) ) for the curve).
Next step would be to take your angle ( A ) that you wish to calculate the cosine of, and do a unitCircleA = A mod PI .
Next, you just run cosOfA = cosPoly(unitCircleA) There you go! I can't recall the exact way to find the interpolation polynom atm, but I will return to you if it pops up. If accuracy is important, just try to increase the number of points ( n ) that are used in your interpolation. Interpolation of n points will give you a polynom of degree n-1 if done right. Also make sure that decimals are preserved all the way through, and that your approximation of PI is detailed enough.
Hope this helps!
Emil Olofsson
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