Question

I need help with this practice problem It is trigonometry

Answer 1

To determine the restriction of the domain of the function tan(x), let us analyze its definition:

$\tan (x)=\frac{\sin (x)}{\cos (x)}$

Because cos(x) goes to zero for values of x equal to ±π/2, for these values we have the limits, in the sense of edge, of the function. After this point tan(x) starts to repeat the values.

Because the edges are given by ±π/2, and the function is not defined in the point, because it becomes a division by 0, we can solve the first part of the problem:

The domain of f(x) = tan( x) is restricted to:

$(-\frac{\pi}{2},\frac{\pi}{2})$

so that the inverse of that function exists. This means that all functional values of f(x) = tan^(-1)( x ) are on the interval:

$\lbrack-\frac{\pi}{2},\frac{\pi}{2}\rbrack$