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Because the trig functions are periodic, every equation has infinitely many solutions. The inverse function gives the principal value, then the symmetry of each function generates the rest: sine repeats with 360° and is symmetric about 90°, cosine is even, and tangent repeats every 180°.
sin x = k
x = arcsin k + 360°n or x = 180° − arcsin k + 360°n
cos x = k
x = ±arccos k + 360°n
tan x = k
x = arctan k + 180°n
The principal solution is 30° and the second in one revolution is 150°.
Its period is 180°, not 360°, so arctan k plus multiples of 180° already covers every solution.