Please solve using basic C and show all work. thanks

Q6. (20 points) (Taylor series) The Taylor series for sin x and cosx are given by 3! 5! 7! x2 x* x 2!4!6! 6 cos Moreover, tan x and cotx are given by sin cos cos Write a C program that calculates the sine, cosine, tangent, and cotangent of a number supplied by the user (x: radian), using the above formulas. Do not use the math library for this problem. You should design your program so that it is accurate to 5 decimal places. For an alternating series, the magnitude of the error is less than the magnitude of the first neglected term. For example, if we use the approximation given by 6 x2 x4 x 2!4!6! cosx-f(x) = 1- then the error is bounded as follows |cos x-f(x)| 8! So, for accuracy to 5 decimal places, we require that