Tan (-pi/2)=what?

1 Answer
Øko
Mar 4, 2018

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

http://www.purplemath.com/modules/triggrph2.htm

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