Inverse functions can be found algebraically by interchanging x and y in the function definition and then making y the subject of the equation. [br][br]They can also be found graphically by reflecting the graph of the function in the line y = x. (Some adjustment may be needed to the domain of the original function to ensure that the inverse function is in fact a function.)[br][br]To produce the inverse of y = cos (x), follow the instructions below the construction.

You will benefit most from this exercise if you attempt to predict what will be produced by each movement of the slider.[br][br]1) Draw the function y = cos(x)[br]2) Draw the line y = x[br]3) Reflect the function in the line[br]4) Choose a region of the domain for y = cos(x) which contains the origin, the curve is monotonic and it covers the full range[br][br]Draw up a table which shows the domain and range for the function and its inverse.