13.1: Inverse trigonometry

In order to calculate an angle given two edges, one uses inverse functions sin⁻¹, cos⁻¹, and tan⁻¹ . (Not to be confused with 1/sin etc.) As functions can, by definition, only map one value to exactly one other value, sin⁻¹ and tan⁻¹ are only defined in the interval [−90°; +90° ] and cos−1 is defined in the interval [0°; 180° ]. This makes it impossible to calculate angles in the 2nd and 3rd, or the 3rd and 4th quadrant, respectively (Figure 13.1). In order to overcome this problem, most programming languages implement a function atan2(opposite,adjacent), which evaluates the sign of the numerator and denumerator, provided as two separate parameters.

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