What if the 1/x key on your calculator is broken ?

Do you know that the trigonometric functions of sin, cosine, tangent and their inverses could be used to simulate the function of the reciprocal key on the calculator ? Believe it or not, this is a valid Math question posed to students of trigonometry!
Enjoy the walkthrough of this fun question, although I don't think you will be putting this into practice anytime soon...