Sine takes an angle and gives a number. To go backwards, from a number to an angle, we need one answer, so sine is restricted to -90° to 90°, where it only rises. On that piece its inverse arcsin exists, and arccos (0° to 180°) and arctan (-90° to 90°) are built the same way. A trig equation like 1.2 sin(30t) + 3.4 = 4 is solved by isolating the sine, taking arcsin for one angle, using the unit circle for the others, and reading each answer back in the gauge's units.