In mathematics, a domain is the set of all input values for which a function is defined. It is the set of all possible values of the independent variable that can be substituted into the function to produce a valid output.
The domain of a tangent function, tan(x), is all real numbers except the values where the cosine function, cos(x), is equal to zero. This is because the tangent function is undefined when the cosine function is equal to zero, as it would result in division by zero.
To find the domain of tan(x/b), we need to determine the values of x that would make the denominator, b, equal to zero. This is because the tangent function is undefined when the denominator is equal to zero. Therefore, the domain is all real numbers except the values of x that make b equal to zero.
Yes, the domain of tan(x/b) can include negative numbers. As long as the value of x does not make the denominator, b, equal to zero, the tangent function is defined for both positive and negative values of x.
If b is equal to zero, the denominator of tan(x/b) would be zero, causing the tangent function to be undefined. Therefore, the domain would be all real numbers except for x=0.