Design and implement a white-box test for a program that computes the sine and cosine functions in a specialized manner. This program is going to be part of an embedded system running on a processor that does not support floating-point arithmetic. The program to be tested is attached. Your job is to test the functions sin and cos; you are to assume that the functions sin0to45 and sin45to90 have already been tested.

Attached Program:

/** These functions compute the sine and cosine of an angle expressed in degrees. The result will be an integer representing the sine or cosine as ten-thousandths. For example, a result of 7071 represents 7071e-4 or 0.7071. */

// Forward declarations int sin0to45(int); int sin45to90(int); int polyEval(int, int[], int);

/** Compute the sine of an angle in degrees. @param x The angle in degrees @return The sine of x */ int sin(int x) { if (x < 0) { x = -x; } x = x % 360; if (0 <= x && x <= 45) { return sin0to45(x); } else if (45 <= x && x <= 90) { return sin45to90(x); } else if (90 <= x && x <= 180) { return sin(180 - x); } else { return -sin(x - 180); } }

/** Compute the cosine of an angle in degrees. @param x The angle in degrees @return The cosine of x */ int cos(int x) { return sin(x + 90); }

/** Compute the sine of an angle in degrees between 0 and 45. pre: 0 <= x < 45 @param x The angle @return The sine of x */ int sin0to45(int x) { // Code to compute sin(x) for x between 0 and 45 degrees // Evaluate a polynomial optimized for this range. int coef[] = { -81, -277, 1747900, -1600}; return polyEval(x, coef, 4) / 10000; }

/** Compute the sine of an angle in degrees between 45 and 90. pre: 45 <= x <= 90 @param x The angle @return The sine of x */ int sin45to90(int x) { // Code to compute sin(x) for x between 45 and 90 degrees // Evaluate a polynomial optimized for this range. int coef[] = { 336, -161420, 75484, 999960000}; return polyEval(90 - x, coef, 4) / 100000; }

/** Function to evaluate a polynomial @param x The point at which the polynomial is to be evaulated @param coef The array of coefficients @param n The number of coefficients (degree + 1) @return x^n-1coef[0] + x^n-2coef[1] + ... x*coef[n-2] + coef[n-1] */ int polyEval(int x, int coef[], int n) { int result = 0; for (int i = 0; i < n; i++) { result *= x; result += coef[i]; } return result; }