Why do these calculators give different angles? ($244^\circ$ vs $-116^\circ$)

Question

Why do these calculators give different angles? How do I fix it?

Answer 1

Note that $244.28^\circ \equiv -155.72^\circ$.

The angles are coterminal, meaning that $244.28^\circ$ and $-155.72^\circ$ are two different ways to express the same angle.

Answer 2

Many "different" angles give the same results for most things: $244°$ works out, for most things, the same as $-116°$ and $604°$ and $-476°$ and many other angles: notice how all the trigonometric functions come out the same for all of those angles. We say all of these angles are equivalent, and that they are all in the same equivalence class. In the particular case of angles, two angles in the same equivalence class are called co-terminal.

Often, when talking about a particular equivalence class, we will select a representative from that class to use and do calculations on. The important part of this is that it must be selected: there isn't generally one always-obviously-right answer! These two calculators have selected their representatives for this equivalence class in two different ways: the Casio has chosen the one that matches $0°\le \theta < 360°$, and the TI has chosen the one that matches $-180° < \theta \le 180°$. To "fix" it, if necessary, you can add or subtract $360°$ to representatives that fall outside your preferred range.