Are $(\sin 49^{\circ})^2$ and $(\cos 49^{\circ})^2$ irrational numbers?
When you enter, $(\sin 49^{\circ})^2$ in a calculator, it shows a long number (and if it is irrational, then clearly the calculator cannot calculate that number to the last digit. i.e., it gives you an approximate for $(\sin 49^{\circ})^2$).
Now save that number in the memory of the calculator, and then calculate $(\cos 49^{\circ})^2$. Now add these numbers up. You will get $1$.
But how this happens?
I am almost sure that the numbers $\sin^2 49^{\circ}$ and $\cos^2 49^{\circ}$ are irrational, and I don't know how does the calculator gives the exact $1$ when you add these up.