Why Are My C/C sin and cos Function Results Inaccurate for Known Angles?

Unexpected Results from sin and cos Functions for Known Angles

When dealing with trigonometric functions like sin and cos in C/C , it's crucial to understand their input requirements. A common misconception is assuming that these functions expect angles in degrees. However, the C/C sin and cos functions require their input angles to be in radians.

To illustrate this, let's consider the given example where an angle of 180 degrees is passed to sin and cos. The expected results, based on trigonometric identities, are:

• sin(180°) = 0.0547
• cos(180°) = 0.99

However, the reported results deviate significantly:

• sin(180°) = 3.5897934739308216e-009
• cos(180°) = -1.00000

The discrepancy arises because the DegreesToRadians() function, rather than performing an exact conversion, provides an approximate result due to rounding and the finite precision of double. Additionally, the constant M_PI representing π is a close, but not precise, approximation.

To improve the accuracy of trigonometric calculations, it's recommended to perform argument reduction in degrees before invoking sin or cos. This process ensures that angles are reduced to a range of -45° to 45° before passing them to the trigonometric functions.

The provided code example demonstrates this technique, reducing the angle to a specified range and then calling the sin function.

extern double sind(double x) {
    // ...
    switch (quo % 4) {
        case 0:
            // Use * 1.0 to avoid -0.0
            return sin(d2r(x90)* 1.0);
        case 1:
            return cos(d2r(x90));
        case 2:
            return sin(d2r(-x90) * 1.0);
        case 3:
            return -cos(d2r(x90));
    }
    return 0.0;
}

This approach yields more precise results for trigonometric calculations, especially for angles near well-known angles like 90°, 180°, etc.

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