Three functions, one angle
sin(45°) ≈ 0.7071067812, cos(60°) = 0.5 exactly, and tan(30°) ≈ 0.5773502692 — each function takes the same kind of input (an angle) and returns a different ratio describing a right triangle containing that angle.
Why degrees get converted to radians first
The underlying math functions (as implemented in virtually every programming language and calculator) work in radians, not degrees — so an angle entered in degrees is first converted to radians using the standard degrees × π/180 formula before the trig function is applied.
Why tangent is sometimes undefined
Tangent is sine divided by cosine, so wherever cosine equals exactly zero — at 90°, 270°, and their equivalents in every full rotation — tangent has no defined value, since division by zero isn't defined.
What these functions don't answer
Sine, cosine, and tangent all go from an angle to a ratio. The reverse question — given a ratio, what angle produced it — is answered by the inverse trigonometric functions, covered in the companion article.