Simple approximations for sine and cosine using recursive identities + small angle approximation and Maclaurin Series

trig-approximations.c

// Math Defs

float factorial (float n) {
    if (n < 1)
        return 1;
    return (n*factorial(n-1));
}

// Approximations Using Trig Identities & Small Angle Formulae

float approxSin (float angle) {
    if (angle < 0.1)
        return angle; // sin x = x
    return 3*approxSin(angle/3) - 4*pow(approxSin(angle/3), 3);
}

float approxCos (float angle) {
    if (angle < 0.1)
        return 1 - (pow(angle, 2)/2); // cos x = 1 - 1/2 (x^2)
    return 4*pow(approxCos(angle/3), 3) - 3*approxCos(angle/3);
}

// Approximations Using Maclaurin Series

float remainderTerm (float x, int n) {
    return pow(x, n+1)/factorial(n+1);
}

float sineHelper (float x, int n) {
    if (n && remainderTerm(x, n) < THRESHOLD)
        return 0;
    return ((n % 2 ? -1 : 1) * (pow(x, 2*n+1)/factorial(2*n+1)) + sineHelper(x, n+1));
}

float sine (float x) {
    int multiplier = x / (2*M_PI);
    x -= (2*M_PI*multiplier);
    return sineHelper(x, 0);
}

float cosHelper (float x, int n) {
    if (n && remainderTerm(x, n) < THRESHOLD)
        return 0;
    return ((n % 2 ? -1 : 1) * (pow(x, 2*n)/factorial(2*n)) + cosHelper(x, n+1));
}

float cosine (float x) {
    int multiplier = x / (2*M_PI);
    x -= (2*M_PI*multiplier);
    return cosHelper(x, 0);
}