since sin ⁡ ⁡ ( θ θ ) ≈ ≈ π π − − θ θ for θ θ ≈ ≈ π π . The solution to this problem involves hyperbolic sinusoids, and note that unlike the small angle approximation, this approximation is unstable, meaning that | θ θ | will usually grow without limit, though bounded solutions are possible. This corresponds to the difficulty of balancing a pendulum upright, it is literally an unstable state.