Does increasing the magnitude of the pendulum angle cause its time period to be underestimated?

Question

The pendulum equation states that the time period $T=2π\sqrt{l/g}$. This is based on the small angle approximation where we approximate l $$\frac{{\rm d}^2 θ}{{\rm d}t^2 }= -\frac{g}{l}\sin θ \approx -\frac{g}{l} θ.$$ So my question is, since the magnitude of $\sinθ$ is smaller than $θ$, through the approximation will the angular acceleration be larger reality, so its speed is overestimated and the time period smaller than without the small-angle approximation?

Answer 1

Yes. The easy way to see this is that physically, as the amplitude approaches 180 degrees, the period must approach infinity.