L 10 6 2 0 -2 -8 -20246 8 10 -10 -10-8-6-4-20 For the other arguments, use the periodicity of the sine or cosine function. sinx = 2 = 3! cosx = 1 – + 5! 7! n=0 (-1)" 2n+1 (2n+1)! (1) 2! 4! 6! n=0 (-1)"2n (2n)! (2)
Write a C
float sinus(float radians, float epsilon);
For your own implementation, use one of the following relations (you only need to program either sine or cosine, you don't need both):
Tip 1: Of course, you cannot calculate the sum of an infinite series indefinitely. You can see (if not, look in the program) that the terms keep getting smaller, so there will definitely be a situation where adding another term will not change the result in any way (see problem 1.3 – machine epsilon). However, you can end the calculation even earlier – when the result changes by less than epsilon (a pre-specified, sufficiently small number, e.g. 0.000001) in two consecutive iterations.
Tip 2: It is important to note that epsilon does not express the accuracy of the calculated approximation.
Tip 3: Be aware that the above series approximate well only around zero, which means that for larger input angles it will "stop working" (see the figure below - the larger the degree of the polynomial, the better the approximation).
For the other arguments, use the periodicity of the sine or cosine function.
AI-generated content may present inaccurate or offensive content that does not represent bartleby’s views.
Unlock instant AI solutions
Tap the button
to generate a solution
