Degrees vs. Radians: When Each Is Used
Degrees divide a full circle into 360 equal parts and are the more intuitive, everyday unit for angles (used in navigation, construction, and most school-level trigonometry); radians measure angles based on the radius of a circle (a full circle equals 2π radians) and are the standard unit in higher mathematics, physics, and programming, because many calculus and trigonometric formulas simplify naturally when expressed in radians.
Using the wrong mode for a given calculation is one of the most common sources of a wildly incorrect trigonometric result, since the same numeric input means a very different angle in each unit.
Why the mode matters so much
Entering sin(90) in degree mode correctly gives 1 (a 90-degree angle), but entering sin(90) in radian mode gives a completely different result, since 90 radians is a huge angle — many multiples of a full circle. Mismatching the expected unit and the calculator's mode is the single most common source of a trigonometric answer that looks obviously wrong.
A practical rule of thumb for choosing
If the angle came from a real-world context described in degrees (a compass bearing, a roof pitch, a school geometry problem), use degree mode; if it came from a formula, a physics equation, or code that already expects radians (many programming language math libraries default to radians), use radian mode.