Isn't that the whole point of programming, being able to translate specifications into code? This is obviously a school assignment (no one in the real world says "but you can't use the math library! OMG!") and you would learn absolutely nothing if I were to write the code for you.
So you need to go to wikipedia, look up arccos and study the formulas give there. Pick one to program and write code for it. Test it by using the Math.Cos function to generate some numbers, then use your code to covert them back.
Just FYI, the last two equations are much easier to program as they don't involve infinite series. And they use System.Numerics and not System.Math :)
What have you tried for yourself?
We are all willing to help you here with your questions, but you got at least show some effort. Momerath has given you all the info you need to get started. So start to program. If you show some of your(even not working) code, we can help you better :)
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