Degrees vs Radians: The Silent Trig Calculator Bug

Every scientific calculator, physical or digital, has an angle-unit setting that quietly changes what every trig function means. Left on the wrong setting, sin(30) can return 0.5 (correct, in degrees) or -0.988 (in radians) — both are 'right answers' to different questions.

Degrees split a circle into 360 parts; radians measure the angle by arc length, so a full circle is 2π radians (about 6.283). A right angle is 90° or π/2 radians (about 1.571) — same angle, different number.

The practical rule: everyday and classroom trigonometry (angles of elevation, construction, navigation) is almost always in degrees. Physics and calculus, especially anything involving derivatives of trig functions, is almost always in radians, because the calculus only works cleanly in radians.

If a trig answer looks wildly wrong — often flipped in sign or scaled by a factor that doesn't obviously relate to your inputs — the angle unit is the first thing to check, before assuming the formula or your arithmetic is at fault.