The sin() command returns the sine of an angle measure. Naturally, the result depends on the angle mode the calculator is in: radian, degree, or (in AMS version 3.10) gradian. You can also use one of the r, °, G marks to specify an angle mode.
For many common angles, sin() can compute an exact result. Other angles, the calculator will leave alone unless it's in approximate mode (or unless you make it approximate), and then it will give a decimal approximation. As long as the calculator is in radian mode, sin() can be used with complex numbers as well.
:sin(30°) 1/2 :sin(x+2π) sin(x) :sin(πi/2) sinh(π/2)*i
If sin() is applied to a list, it will take the sine of every element in the list.
The sin() of a matrix is not (in general) the same as taking the sine of every element of the matrix. A different definition is used to compute the result; see Matrices and Their Commands. It requires the matrix to be square and diagonalizable in order to apply.
230 - Dimension happens when taking sin() of a matrix that isn't square.
260 - Domain error happens when taking sin() of a complex number in degree or gradian mode.
665 - Matrix not diagonalizable happens when taking sin() of a matrix that isn't diagonalizable.