Question: Prove that the discrete-time dynamical system xt+1 = cos(xt) has an equilibrium between 0 and /2. The Intermediate Value Theorem can often be used to

Prove that the discrete-time dynamical system xt+1 = cos(xt) has an equilibrium between 0 and π/2.
The Intermediate Value Theorem can often be used to prove that complicated discrete-time dynamical systems have equilibria.

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