Radian symbol, and in mathematical writing the symbol "rad" is almost always omitted. When quantifying an angle in the absence of any symbol, radians are assumed, and when degrees are meant the symbol ° is used. It follows that the magnitude in radians of one complete revolution (360 degrees) is the length of the entire circumference divided by the radius, or , or 2. Thus 2 radians is equal to 360 degrees, meaning that one radian is equal to 180/ degrees. The relation formula_1 can be derived using the formula for arc length. Taking the formula for arc length, or formula_2.
Degrees of freedom (statistics) the vectors of residuals are constrained to lie in a space of smaller dimension than the number of components in the vector. That smaller dimension is the number of degrees of freedom for error, also called residual degrees of freedom. Perhaps the simplest example is this. Suppose are random variables each with expected value μ, and let be the "sample mean." Then the quantities are residuals that may be considered estimates of the errors "X" − μ. The sum of the residuals (unlike the sum of the errors) is necessarily 0. If one knows the values of any "n" −