Question

Tan (-pi/2)=what?

Answer 1

See explanation

Explanation:

By the definition of tangent

`tan(x)=sin(x)/cos(x)`

So for `tan(-pi/2)`

`tan(-pi/2)=sin(-pi/2)/cos(-pi/2)=-1/0`

Which is undefined (division by 0)

However the limit must be

`lim_(x->(-pi/2)^+)=tan(x)=sin(x)/cos(x)=-oo`

`lim_(x->(-pi/2)^-)=tan(x)=sin(x)/cos(x)=oo`

Which we also can see if we graph tangent