Your calculator should have arcsin (sometimes abbreviated to asin) or sin₋⁻¹. This is usually located over the sin button and requires you to operate the SHIFT button before pressing the arcsin button followed by the value you wish to apply it to. Similarly for cos and tan.
If you mean by inverse sec, cosec (csc) and cot, the calculator should have a 1/x button. Activate it then type in cos, sin, tan (as appropriate) followed by the angle in radians or degrees, as appropriate. The result will be sec, csc, cot respectively. Note that tanθ is the same as cot(90-θ) where θ is in degrees, or cot(π/2-θ) where θ is in radians.