Difference between reciprocal and inverse notation trig functions

Reciprocal is just 1 / (function) example, the reciprocal of cos (x) is 1/cos (x)

inverse is the oposite of it, it is the original function reflected across the y=x line

the inverse of cos (x) is cos⁻¹ (x)

they are inverse because if cos (x) = y then cos⁻¹ (y) = x