Four polynomials are shown below…

The functions are the inverses of tangent, sine, and cosine, also called arctan, arcsin, and arccos.

For an angle θ that is not the right angle of the triangle (I’m only talking about first quadrant)

arctan of a number, which is like arctan(1), will tell you the angle θ in which tan θ = 1, which in this case is π/4

arcsin of a number will tell you the angle θ in which sin θ= that number, like arcsin(1/2)= π/6 because sin(π/6)=1/2

arccos of a number will tell you the angle θ that the cos θ=that number, like arccos(1/2)= π/3 because cos(π/3)=1/2

So in general, for angle θ that is not the right angle of the triangle,
arctan(opposite/adjacent)=θ
arcsin(opposite/hypotenuse)=θ
arccos(adjacent/hypotenuse)=θ