3. Nested Loops Write a Java program that uses a for loop to approximate cos(x) using the following Taylor series expansion: 2 pan 77 cos(x) = (-1)" ) This program should use an x of, and should calculate the approximate value based on 6 the series expansion. The actual value of cosine and the approximation should both be printed to the console with descriptive text. All cosine values should be displayed with 16 decimal places. The value of n should be experimented with to show the number of terms needed to provide an accurate approximation to 15 digits. Try to determine (intuitively through experimentation) when the cost of calculating outweighs the increase in accuracy. In a comment below your code, describe why you are seeing the behavior observed during the approximation. Consider if the series converges or diverges, how quickly that happens, and factors that might influence why that happens. At what point is the cost of calculation going to outweigh any increases in accuracy? Show a working version of this program to the instructor before moving on