When should the inverse sin, cos and tan be used? Provide example please

When you know sin, cos, tan of angle and want to find angle.
Or when you have side measures of right triangle, and want to find angle.

For example, say you have a right triangle with side 3, 4, 5
You want to find angle θ opposite side of length 4
We know that sin(θ) = 4/5, cos(θ) = 3/5, tan(θ) = 4/3
So θ = sin⁻¹(4/5) or cos⁻¹(3/5) or tan⁻¹(4/3) = 53.13°

when you have to calculate an angle, for example

cos 60 = 1/2
so cos inverse 1/2 = 60 degrees

tan 60 = sqrt(3)

therefore tan inverse sqrt(3) = 60 degrees

sin30 = 1/2
therefore sin inverse 1/2 = 30 degrees

when you have an angle measure instead of a side measure