# Tan (-pi/2)=what?

##### 1 Answer

Mar 4, 2018

See explanation

#### Explanation:

By the definition of tangent

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

So for

#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