Definitions: The sine (or sin), cosine (or cos) and tangent (or tan) functions are defined as returning the following ratios: These ratios are functions of θ because x and y change with θ. |
These formulas are called polynomial approximations and are based on Taylor's series. To use them x must be in radians. They are very accurate when x is close to 0 but lose accuracy as x gets bigger. When x = π/4 radians (i.e. 45°) the sin formula is only accurate to within ±0.00004, cos to within ±0.000004 and tan to within ±0.004.