Acalculator is broken so that the only keys that still work are the sin, cos, tan, cot, sin^-1, cos^-1, and tan^-1 buttons. the display initially shows 0. in this problem, we will prove that given any positive rational number q, show that pressing some finite sequence of buttons will yield q. (assume that the calculator does real number calculations with infinite precision. all functions are in terms of radians.)
(a) find a sequence of buttons that will transform x into 1/x.
(b) find a sequence of buttons that will transform sqrt(x) into sqrt(x+1).