True or False: For a trigonometric function, y=f(x), then x= F^-1(y).

Question

Please explain how you get the answer

Answer 1

False.

Counter example:

y = sin θ

y = sin π/6

y = 0.5

 

arcsin 0.5 = π/6 and 5π/6 (and multiple other values!)

 

The inverses of the trigonometric functions are functions only over a restricted domain.