(Numerical) For small values of x, the value of sin(x) can be approximated by this po...

(Numerical) For small values of x, the value of sin(x) can be approximated by this power series:

As with the sin ( ) function, the value of x must be in radians. Using this power series, write, compile, and execute a C++ program that approximates the sine of 180/3.1416 degrees, which equals one radian. Additionally, have your program use the sin ( ) function to calculate the sine and display both calculated values and the absolute difference of the two results. Manually verify the approximation your program produces. After verifying that your program is working correctly, use it to approximate the value of the sine of 62.2 degrees.