Degrees are for humans. Radians are for math. Calculus loves them; trigonometry needs them done right.
Most people learn the formula once in school and never touch it again — until life forces them to. Degrees are for humans. Radians are for math. Calculus loves them; trigonometry needs them done right.
1 radian = the angle that subtends an arc equal to the radius. 2π radians = 360°.
deg × π/180 = rad. rad × 180/π = deg.
Small-angle approximations work: sin(x) ≈ x when x is in radians.
What's a gradian? 1/400 of a full turn. Surveyors use them. Most people never need to.
Why isn't 360 a more natural number? It's divisible by 24 of the first 28 integers — handy for fractions, but mathematically arbitrary.
If you only remember one thing from this post, make it that the inputs matter more than the calculator.