A calculator is broken so that the only keys that still work are the sin, cos, tan, cot, asin, acos, and atan buttons. Assume that the calculator does real number calculations with infinite precision. All functions are in terms of radians.
(a) Find, with proof, a sequence of buttons that will transform x into 1/x.
(b) Find, with proof, a sequence of buttons that will transform sqrt(x) into sqrt(x+1).
(c) The display initially shows 0. Prove that there is a sequence of buttons that will produce 3/sqrt(5).
Provided x can be entered, and
if the calculator uses the reverse polish notation then:
a) \( \frac{1}{x}\) \(x \Rightarrow atan \Rightarrow cot\) \(\frac{1}{x}=cot(atan (x)) \) \(x \in \{x|x\in\mathbb {R}\}\)
Works with DEG and RAD.
I pass.
!